Search

The work explores the optical wave solutions along with their graphical representations by proposing the coupled spatial-temporal fractional cubic-quartic nonlinear Schrödinger equation with the sense of two fractal derivatives (beta and conformable derivative) and Kerr law nonlinearity for birefringent fibers. The new extended direct algebraic method for the first time is implemented to achieve this goal. Many optical solutions are listed along with their existence criteria. Based on the existence criteria, the cubic-quartic bright, and singular optical soliton, periodic pulse, and rouge wave profiles are supported in birefringent fibers with the influence of both beta and conformable derivative parameter.

The brake mechanism is one of the inevitable and safety-critical components in an automobile. A proper rotor design and superior heat dissipating material provide better performance during the braking mechanism. In this study, modified ventilated disk brake rotor has been developed with curved vents, holes, and slots and analyzes the stress and temperature distribution. Finite element models of the rotor are shaped with SolidWorks and simulated using ANSYS. Structural and thermal characteristics are compared with a reference disk brake rotor. It is found that the proposed rotors outperformed the conventional one in terms of stress generation, temperature distribution, and factor of safety. Furthermore, computation has been done to find out the best-suitedmaterial for one of the proposed designs. The result provides a physical insight of the structural and thermal characteristics of the geometrically modified rotor that can be implemented in the automotive industry.

This work deals with the ion-acoustic shock waves (IASWs) around the critical values in an unmagnetized pair–ions plasma with ( $$\alpha , q$$ )-distributed electrons by formulating the correct stationary solution of Burgers-type equations with higher-order corrections. By considering higher-order correction of the reductive perturbation technique, the modified Burgers(mB)-, and mixed modified Burgers(mmB)-type equations are derived. With the changes of viscosity coefficients of positive and negative ions, the electrostatic IASWs and normalized electric fields are investigated around the critical values. The current studies might be very useful to understand the behavior of shocks around the critical values in the F- and D-regions of Earth’s ionosphere, and the later experimental verification in plasma laboratory.

This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials.

This paper explores the head-on collision between two-counter propagating positron acoustic solitons and double layers (DLs) in an unmagnetized collisionless plasma having mobile cold positrons fluid, immobile positive ions and ($$r,\;q$$ r , q )-distributed hot positrons, and hot electrons. By employing the extended Poincaré–Lighthill–Kuo method, the coupled Korteweg–de Vries (KdV), modified KdV (mKdV) and Gardner equations are derived to archive this goal. The effect of dimensionless parameters on the propagation characteristics of interacting KdV solitons (KdVSs), mKdV solitons (mKdVSs), Gardner solitons (GSs) and DLs are examined in detail by considering the limiting cases of ($$r,\;q$$ r , q )-distribution. It is noted that the interaction of GSs and DLs are reported for the first time. The outcomes might be comprehended and beneficial not only in space and astrophysical environments but also in laboratory studies.

This paper explores the head-on collision between two-counter propagating positron acoustic solitons and double layers (DLs) in an unmagnetized collisionless plasma having mobile cold positrons fluid, immobile positive ions and ([Formula: see text])-distributed hot positrons, and hot electrons. By employing the extended Poincaré-Lighthill-Kuo method, the coupled Korteweg-de Vries (KdV), modified KdV (mKdV) and Gardner equations are derived to archive this goal. The effect of dimensionless parameters on the propagation characteristics of interacting KdV solitons (KdVSs), mKdV solitons (mKdVSs), Gardner solitons (GSs) and DLs are examined in detail by considering the limiting cases of ([Formula: see text])-distribution. It is noted that the interaction of GSs and DLs are reported for the first time. The outcomes might be comprehended and beneficial not only in space and astrophysical environments but also in laboratory studies.

The head-on collision between two-counter-propagating electron acoustic solitons and double layers (DLs) in an unmagnetized collisionless multi-species plasma consisting of inertial cold electron fluid and ( α, q)-distributed hot electrons and positrons has been analyzed with the stationary background of massive positive ions. For nonlinear analysis of colliding wave phenomena, the coupled Korteweg–de Vries equation (KdVE), modified KdVE (mKdVE), and standard Gardner equation have been derived by adopting the extended Poincaré–Lighthill–Kuo technique. The effect of non-dimensional parameters on the collisional KdV, mKdV, and Gardner solitons (GSs) and DLs has been examined in detail by considering the limiting cases of ( α, q)-distributions. It is found that the plasma model supports (i) the compressive and rarefactive collisional KdV solitons and GSs, (ii) only compressive mKdV solitons, and (iii) only rarefactive collisional DLs. The rarefactive collisional solitons are more affected by nonextensivity and the increase of the temperature of electrons than their compressive counterpart, whereas the rarefactive collisional DLs only existed in the presence of nonthermality.

This chapter deals with the ion-acoustic (IA) solitons, rogue waves (RWs), and double layers (DLs) in multi-component plasmas consisting of positively charged ion fluid and \((\alpha , q)\)-distributed electrons as well as positrons. The nonlinear evolution equations, namely, Korteweg–de Vries equation (KdVE), modified KdV equation (mKdVE), nonlinear Schrodinger equation (NLSE) and standard Gardner equation (SGE) along with their solutions are derived using the reductive perturbation method. It is examined that KdV, and SG solitons, RWs and DLs are supported both of positive and negative electrostatic potential structures, but mKdV supports only negative electrostatic potential structure by depending on the related plasma parameters. The outcomes presented may be very helpful in understanding the behavior of nonlinear coherent structures in many astrophysical and space environments and the future experimental studies in laboratory.

This article examines the essential phenomena of nonlinear ion-acoustic waves (IAWs) in the unmagnetized relativistic collisionless plasmas by considering generalized distributed electrons, Boltzmann distributed positrons, and relativistic ions having kinematic viscosity. The nonlinear electrostatic IA shock and solitary wave dynamics are conducted by new nonlinear evolution equations, such as Korteweg-de Vries (KdV)–Burgers-type Schamel equation and the well-known KdV-type Schamel equation, respectively, due to the involvement of superthermal electrons, having trapping efficiency and kinematic viscosity of ions. It is first time reported that the nonlinear IAWs are supported by only positive polarity shock structures and solitons for superthermal electrons, having trapping efficiency with and without the influence of kinematic viscosity of ions, respectively, in the relativistic plasmas.

The plane waves with their dynamical behaviors of (2+1)-dimensional nonlinear Schrodinger equation (NLSE) having beta derivative spatial-temporal evolution are investigated. In order to study such phenomena, NLSE is converted to a nonlinear ordinary differential equation with a planar dynamical system (PDS) by considering the variable wave transform and the properties of the beta derivative. By employing two distinct solution methods, namely, the auxiliary ordinary differential equation method and the extended simplest equation method, some more new general form of analytical solutions of NLSE are constructed. The effect of beta derivative parameter and obliqueness on several types of wave structures along with the phase portrait diagrams are reported. It is found that the PDS is not supported by any type of orbits for Θ = 45°. It is also confirmed from the obtained solutions that no plane waves are generated for Θ = 45°. The presented studies on bifurcation analysis and analytical solutions for (2+1)-dimensional NLSE would be very useful to understand the physical scenarios for Heisenberg models of ferromagnetic spin chain with magnetic interactions.

This work intends to focus on the dynamical behaviors for the discrete nonlinear electrical transmission line(NETL) with the presence of Caputo-Fabrizio fractional derivative. With the changes of some parameters for the local solution and the nonlocal solution of NETL, the results are analyzed based on the response of bifurcation diagrams. It is immersed that the stability state in the local derivative has converted to a durable, stable spiral node in Caputo-Fabrizio fractional derivatives, which is a notable outcome of this exertion.

This work studies fractional temporal evolution of oblique resonant optical solitons in (3+1)-dimensions with Kerr- and parabolic-law nonlinearities. The generalized exp(−Φ(ξ))-expansion method along with the Khalil's conformable fractional derivatives is implemented to locate several forms of oblique resonant solitons. It is observed that obliqueness significantly modified resonant wave dynamics. The obtained results are very useful for understanding the dynamics of obliquely propagating resonant optical solitons and optical bullets.

This work investigates the basic features of Nonlinear Ion Acoustic Solitary waves (NIASWs) and their dynamical behaviours in an unmagnetized relativistic collisionless plasma system via the Schamel Korteweg-de Vries (SKdV) equation. Such plasma is composed by the generalized distributed electrons, Boltzmann distributed positrons and relativistic warm ions. The influences of plasma parameters on NIASWs and their dynamical behaviours are investigated by comparing 26−term expansion of relativistic Lorentz factor (RLF) with both of weakly (2−term expansion of RLF) and highly (3−term expansion of RLF) regimes. It is found that the 26−term expansion of RLF are significantly changed NIASWs instead of both weakly and highly relativistic regimes. Therefore, the theoretical results would be very useful for understanding the nature (amplitude, width, polarity, etc.) of wave dynamics not only in astrophysical and space environments but also in further laboratory studies, where the proposed plasma assumptions are existed.

This work investigates the interactions among ion acoustic (IA) single- and multi-soliton and their corresponding phase shifts in an unmagnetized plasma composed of degenerate electrons, positrons, and positive ions. Two-sided Korteweg-de Vries (KdV) equations are derived by employing the extended Poincare-Lighthill-Kuo (PLK) method for the stretched coordinates. The single- and multi-soliton solutions of the KdV equations are constructed by using the Hirota’s method. The phase shifts are determined for two-, four-, six-, and eight-IA scattering solitons. The effect of positron concentration on electrostatic IA resonances due to the interactions among solitons and their corresponding phase shifts are investigated.

The oblique plane waves with their dynamical behaviors for a (2+1)-dimensional nonlinear Schrödinger equation (NLSE) having beta derivative spatial-temporal evolution are investigated. In order to study such phenomena, NLSE is converted to a nonlinear ordinary differential equation with a planar dynamical system by considering the variable wave transform with obliqueness and the properties of the beta derivative. Some more new general forms of analytical solutions, like bright, dark, singular, and pure periodic solutions of NLSE are constructed by employing the auxiliary ordinary differential equation method and the extended simplest equation method. The effect of obliqueness and beta derivative parameter on several types of wave structures along with the phase portrait diagrams are reported by considering some special values of parameters for the existence of attained solutions. It is found that the planar dynamical system is not supported by any type of orbit for

The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations (NLEEs) arising in science and engineering. The conformable time fractional (2 + 1)-dimensional extended Zakharov-Kuzetsov equation (EZKE), coupled space-time fractional (2 + 1)-dimensional dispersive long wave equation (DLWE) and space-time fractional (2 + 1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation are considered to investigate such physical phenomena. The modified Kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered equations. The obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering. Keywords: Fractional nonlinear evolution equations, Conformable derivative, Modified kudryashov method, Oblique wave solutions, MSCClassification codes: 35E99, 35N05, 35Q40

This work investigates the obliquely propagating wave solutions of conformable time fractional (2 + 1)-dimensional extended Zakharov–Kuzetsov equation (eZKE) for understanding the behavior of physical issues in science and engineering, especially in magnetized plasmas. The generalized exp(− Φ(ξ))-expansion method along with the conformable fractional derivatives is employed to obtain various types of exact solutions to eZKE. The traveling wave solutions of eZKE are represented in the forms of hyperbolic, trigonometric and rational functions with physical as well as some additional free parameters. It is found that the obliqueness and physical parameters are significantly modified the wave dynamics taking the appropriate values of free and physical parameters.

We wish to point out a mistake in the paper [Indian J Phys 90, 603 (2016)], which partially changes a few results presented.

The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the (G'/G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.

This work investigates the obliquely propagating resonance wave phenomena described by coupled model equations with fractional temporal evolution arising in many branches of physics. The (2 + 1) -dimensional coupled nonlinear Schrodinger equation (NLSE), long wave-short wave resonance interaction (LSRI) equation and Maccari system (MS) having fractional time evolution are considered to study such physical phenomena. The modified Kudryashov method (mKM) with the properties of Khalil's conformable fractional derivatives is implemented to divulge scattered oblique wave solutions of considered equations. The effects of obliqueness and fractional parameter on obtained results are demonstrated graphically along with the physical descriptions. It is found that the resonance wave phenomena are changed with the increase of obliqueness as well as fractional parameter.

In this article, the oblique resonance wave phenomena are investigated by considering nonlinear coupled evolution equations with fractional time evolution. In order to investigate such physical phenomena arising in many branches of physics, the time fractional coupled (2 + 1)-dimensional nonlinear Schrodinger and long-short wave resonance interaction evolution equations are considered. The analytical solutions of considered equations are achieved by implementing the proposed auxiliary ordinary differential equation method along with the properties of Khali’s fractional derivatives. The obtained outcomes may be useful for better understanding the basic properties of internal oblique propagating wave dynamics in many branches of science and engineering.

In this paper, the novel (G′/G)-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.

In this article, the oblique resonant traveling waves and dynamical behaviors of (2+1)-dimensional Nonlinear Schrodinger equation along with dual-power law nonlinearity, and fractal conformable temporal evolution are reported. The considered equation is converted to an ordinary differential equation by taking the traveling variable wave transform and properties of Khalil's conformable derivative into account. The modified Kudryashov method is implemented to divulge the oblique resonant traveling wave of such an equation. It is found that the obliqueness is only affected on width, but not on amplitude and phase patriots of resonant nonlinear propagating wave dynamics. The research outcomes are very helpful for analyzing the obliquely propagating nonlinear resonant wave phenomena and their dynamical behaviors in several nonlinear systems having Madelung fluids and optical bullets.

This work investigates the wave-wave interactions by considering two-sided time fractional Korteweg-de Vries equations (TFKdVEs). The generalized $\exp(-\Phi(\xi))$ -expansion method (GEEM) along with Khalil's fractional derivatives is employed to divulge several types of scattered wave solutions of TFKdVEs. It is found that the fractional parameters significantly modified the interaction of nonlinear wave dynamics. The results obtained may be useful for clarifications of the interaction between two waves not only in non-conservative fluid-filled elastic tubes but also in shallow water and plasma physics.

The head-on collision between positron acoustic solitary waves (PASWs) as well as the production of rogue waves (RWs) in homogeneous and PASWs in inhomogeneous unmagnetized plasma systems are investigated deriving the nonlinear evolution equations. The plasmas are composed of immobile positive ions, mobile cold and hot positrons, and hot electrons, where the hot positrons and hot electrons are assumed to follow the Kappa distributions. The evolution equations are derived using the appropriate coordinate transformation and the reductive perturbation technique. The effects of concentrations, kappa parameters of hot electrons and positrons, and temperature ratios on the characteristics of PASWs and RWs are examined. It is found that the kappa parameters and temperature ratios significantly modify phase shifts after head-on collisions and RWs in homogeneous as well as PASWs in inhomogeneous plasmas. The amplitudes of the PASWs in inhomogeneous plasmas are diminished with increasing kappa parameters, concentration and temperature ratios. Further, the amplitudes of RWs are reduced with increasing charged particles concentration, while it enhances with increasing kappa- and temperature parameters. Besides, the compressive and rarefactive solitons are produced at critical densities from KdV equation for hot and cold positrons, while the compressive solitons are only produced from mKdV equation for both in homogeneous and inhomogeneous plasmas.

The novel (G′/G)-expansion method is one of the powerful methods accredited at the present time for establishing exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, the method has been implemented to find the traveling wave solutions to the positive Gardner-KP equation. The efficiency of this method for finding exact and traveling wave solutions has been demonstrated. The obtained solutions have been compared with the solution obtained by other methods. The solutions have also been demonstrated by figures. It has been shown that the method is straightforward and an effective tool for solving NLEES that occur in applied mathematics, mathematical physics, and engineering.

In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.

The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas–Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.

The theoretical and numerical studies have been investigated on nonlinear propagation of weakly relativistic ion acoustic solitary waves in an unmagnetized plasma system consisting of nonextensive electrons, positrons and relativistic thermal ions. To study the characteristics of nonlinear propagation of the three-component plasma system, the reductive perturbation technique has been applied to derive the Korteweg–de Vries equation, which divulges the soliton-like solitary wave solution. The ansatz method is employed to carry out the integration of this equation. The effects of nonextensive electrons, positrons and relativistic thermal ions on phase velocity, amplitude and width of soliton and electrostatic nonlinear propagation of weakly relativistic ion acoustic solitary waves have been discussed taking different plasma parameters into consideration. The obtained results can be useful in understanding the features of small amplitude localized relativistic ion acoustic solitary waves in an unmagnetized three-component plasma system for hard thermal photon production with relativistic heavy ions collision in quark–gluon plasma as well as for astrophysical plasmas.

The exp(?(?))-expansion method is applied to find exact traveling wave solutions to the (2+1)-dimensional Boussinesq equation which is an important equation in mathematical physics. The traveling wave solutions are expressed in terms of the exponential functions, the hyperbolic functions, the trigonometric functions and the rational functions. The procedure is simple, direct and constructive without the help of a computer algebra system. The applied method will be used in further works to establish more new solutions for other kinds of nonlinear evolution equations arising in mathematical physics and engineering.

In this article, the novel (G′/G)-expansion method is used to construct exact travelling wave solutions of the coupled nonlinear evolution equation. This technique is uncomplicated and simple to use, and gives more new general solutions than the other existing methods. Also, it is shown that the novel (G′/G)-expansion method, with the help of symbolic computation, provides a straightforward and vital mathematical tool for solving nonlinear evolution equations. For illustrating its effectiveness, we apply the novel (G′/G)-expansion method for finding the exact solutions of the (2 + 1)-dimensional coupled integrable nonlinear Maccari system.

In this article, the exp(− Φ ( ξ ))-expansion method has been successfully implemented to seek traveling wave solutions of the coupled Higgs field equation and the Maccari system. The result reveals that the method together with the first order ordinary differential equation is a very influential and effective tool for solving coupled nonlinear partial differential equations in mathematical physics and engineering. The obtained solutions have been articulated by the hyperbolic functions, trigonometric functions and rational functions with arbitrary constants. Numerical results together with the graphical representation explicitly reveal the high efficiency and reliability of the proposed algorithm.

The novel ( G ′/ G )-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein–Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel ( G ′/ G )-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs) in applied mathematics, mathematical physics and engineering.

In this paper we introduce a formal theory on unveiling relativistic effects during electron emission from clean metallic surfaces upon high charged particle impact using a Jellium-type wave function including suitable spinors. In addition image charge final state electron surface interactions have been initiated in the relativistic region as well as the scattering of the projectile from the multi-center bulk potential. Finally, a semi-relativistic condition is considered in place of the ionization mechanism of scattering from an aluminium semi-infinite solid target by non-relativistic electrons to determine multiple differential cross-section.

This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries (KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influence of plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequency waves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.

This work investigates the oblique nonlinear propagation of ion acoustic (IA) shock waves for both weakly and highly relativistic plasmas composed of nonthermal electrons and positrons with relativistic thermal ions. The KdVB-like equation, involving dispersive, weakly transverse dispersive, nonlinearity and dissipative coefficients, is derived employing the well known reductive perturbation method. The integration of this equation is carried out by the $\mathit{tanh}$ method taking the stable shock formation condition into account. The effects of nonthermal electrons and positrons, nonthermal electrons with isothermal positrons, isothermal electrons with nonthermal positrons, and isothermal electrons and positrons on oblique propagation of IA shock waves in weakly relativistic regime are described. Furthermore, the effects of plasma parameters on oblique propagation of IA shock waves in highly relativistic regime are discussed and compared with weakly relativistic case. It is seen that the plasma parameters within certain limits significantly modify the structures of the IA shock waves in both cases. The results may be useful for better understanding of the interactions of charged particles with extra-galactic jets as well as astrophysical compact objects.

The aim of this comment is to show the solution of the KdVB equation used by Shah et al. (Astrophys. Space Sci. 335:529–537, 2011, doi: 10.1007/s10509-011-0766-y ) is not correct. So, the numerical results that are predicted in this manuscript should not be helpful for further investigations in a plasma laboratory. For this reason, we have employed the Bernoulli’s equation method to obtain the correct form of analytical solution to this equation, which is appropriate for the study of electrostatic compressive and rarefactive shocks and solitons in relativistic plasmas occurring in polar regions of pulsar.

The theoretical investigations have been made for the propagation of positron acoustic solitary waves (PASWs) in a weakly inhomogeneous plasma composing immobile positive ions, mobile cold positrons, and superthermal hot positrons and electrons. The Korteweg-de Varies (KdV) and modified KdV (mKdV) equations with variable coefficients are derived using the appropriate coordinate transformation and the reductive perturbation method (RPM). The effects of positron concentration, temperature ratios for hot positrons and electrons, hot to cold positrons density ratio, electron to cold positron density ratio, ion to cold positron density and population of hot electrons as well as positrons superthermality on the nonlinear propagation of PASWs are examined to understand the local electrostatic disturbances. It is also found that the presence of superthermal (kappa distributed) hot positrons and hot electrons significantly modify the basic features of PASWs. The critical values for hot positrons and cold positrons also play a vital role in the formation of only compressive PASWs in the plasmas.

Head-on collision between ion acoustic shock waves (IASWs) and the consequences after collision are investigated considering the plasma system to be consisting of relativistic warm ions and nonextensive electrons and positrons, taking into account the effects of nonlinearity and dispersion. Two-sided KdV-Burger equations are derived employing the extended Poincar e ´-Lighthill-Kuo method. The results reveal that the plasma parameters are responsible for the modification of the structures along with phase shifts of the shock waves. The nonlinearity effects on IASWs in a highly relativistic regime (HRR) become pronounced rather than the weakly relativistic regime (WRR). The phase shifts of IASWs are enhanced by the relativistic streaming factor and superthermality. The electrostatic IASWs become rarefactive depending on temperatures, kinematic viscosity, and superthermality in both WRR and HRR. The amplitudes of IASWs are increasing for WRR but decreasing for HRR due to increasing ion thermal velocities. Besides, the amplitudes of the solitons are detaining due to the increase in the positron concentration for the depopulation of ions.

The propagation characteristics and interactions between the dust acoustic (DA) one and multi solitons in an unmagnetized dusty plasmas composing negatively charged mobile dust, Boltzmann distributed electrons, nonextensive distributed cold and nonthermal distributed hot ions are studied. The well known extended Poincar Lighthill Kuo (PLK) method is employed to derive the two sided Korteweg de Vries (KdV) equations. The solutions of KdV equations are constructed using the Hirota method both for one and multi solitons. The phase shifts are determined for the interaction of one, two and three DA solitons. The effects of plasma parameters on the head on collision of DA one as well as multi solitons and their corresponding phase shifts are investigated.

A comparative study of the interactions between nonlinear ion acoustic solitary waves (IASWs) propagating toward each other, and the electrostatic nonlinear propagation of IASWs, both for the weakly and relativistic regimes consisting of relativistic warm ions, nonthermal electrons, and positrons, is carried out. Two-sided Korteweg–de Vries (KdV) equations are derived using the extended Poincare-Lighthill-Kuo (PLK) method to reveal the physical issues concerned. The effects of positron concentration, ion-electron temperature ratio, electron-positron temperature ratio, relativistic streaming factor, the population of electron, and positron nonthermality on the electrostatic resonances and their phase shifts are investigated for both regimes. It is found that the plasma parameters significantly modify the phase shifts, electrostatic resonances, hump-shaped electrostatic potential profiles, and the electric fields on the nonlinear propagation characteristics of IASWs. The results obtained may be useful for c...

A comparative study is carried out for the nonlinear propagation of ion acoustic shock waves both for the weakly and highly relativistic plasmas consisting of relativistic ions and q-distributed electrons and positions. The Burgers equation is derived to reveal the physical phenomena using the well known reductive perturbation technique. The integration of the Burgers equation is performed by the method. The effects of positron concentration, ion–electron temperature ratio, electron–positron temperature ratio, ion viscosity coefficient, relativistic streaming factor and the strength of the electron and positron nonextensivity on the nonlinear propagation of ion acoustic shock and periodic waves are presented graphically and the relevant physical explanations are provided.

The characteristics of the nonlinear oblique propagation of ion acoustic solitary waves in unmagnetized plasmas consisting of Boltzmann positrons, trapped electrons and ions are investigated. The modified Kadomtsev-Petviashivili ( mKP) equation is derived employing the reductive perturbation technique. The parametric effects on phase velocity, Sagdeev potential, amplitude and width of solitons, and electrostatic ion acoustic solitary structures are graphically presented with the relevant physical explanations. This study may be useful for the better understanding of physical phenomena concerned in plasmas in which the effects of trapped electrons control the dynamics of wave.

The Korteweg-de Vries Burgers (KdVB)-like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.