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We purpose an approach for the thermodynamic analysis of a rotating and non-linear magnetic-charged black hole with quintessence. Accordingly, we compute various thermodynamic quantities of the black hole, such as mass, temperature, potential provided from the magnetic charge, and the heat capacity. This allows us to appreciate how quintessence modifies the behaviour of the black hole. Moreover, we study second-order phase transitions of this black hole, analysing the plot of its heat capacity. Then, we show that the black hole mass would have a phase of decrease. From the behaviour of the heat capacity, we point out that the black hole undergoes to a second-order phase transition, which is shifted towards higher values of entropy as we increase the rotating parameter a or the magnetic parameter Q. However, we have found that when we increase the quintessence parameter c, the second-order phase transition is instead shifted to lower entropy values.

In this work, under consideration is the coupled system of nonlinear Schrödinger (NSL) and Boussinesq equations that serves as model to study the polarization fluctuation in α-helical protein. M-shaped and W-shaped solutions have been derived through the new modified Sardar sub-equation technique (SSEM). These solitons solutions define the polarization dynamics in the α-helical protein. The integration naturally leads to a constraint condition placed on the solitary wave variables which must hold for the solitary waves to exist. In addition, the standard linear stability analysis has permitted to study the behavior of the Modulation Instability (MI) gain spectra. Numerical simulation and physical interpretations of the acquired results are demonstrated. The derived structure of the acquired solutions give a rich platform to better understand the nonlinear dynamics in the α-helical protein.

A pseudo-Hermitian (PH) system made up of three coupled waveguides (trimer) with an overall balanced gain and loss is investigated in a parity time (PT)-symmetric-like regime. Remarkably, the pseudo hermiticity parameter controls the asymmetric spatial field modulation between left and right propagating waves whereby, a complex coupling arises that induces an additional source of non-Hermiticity, which in the system acts as a relative gain/loss Hellmann-Feynman correction. In this situation, we show that, transmissionless backscatterings are observed for the PH-trimer in the non PT broken phase. Interestingly, the scattering properties of PH-trimer result in multiple lasing states with different mechanisms. In particular, we show that in the PT-symmetric case, the lasing modes associated to the coherent perfect-absorption (CPA), occur from the spectral singularity induced by the Hermitian chain coupling and give rise to unidirectional invisibility in the direction of incident wave. On the contrary, additional emerging lasing modes in a PH regime result from the scattering maxima resonance. We demonstrate that this specific cases suppress the CPA-laser phenomenon and rather exhibit exceptional points characterized by reflectionless but also the points of transmissionless. Numerical beam propagations realized to emphasize the results are in good agreement with the scattering investigation until gain/loss parameter is around it’s value giving resonance.

This paper investigates the new periodic wave solutions for the third-order (2 + 1)-dimensional equation, which describes the wave propagation in shallow water, using the Hirota bilinear method and a three-wave method. The Lump Periodic wave, soliton periodic wave, and breather periodic have been represented by the three-dimensional images and contour images, by choosing the appropriate parameters, illustrating these solutions. The influence of the surface tension on the dynamics of the wave is also studied.

We report in this paper a detailed analysis of modulational instability of a plane wave solution of discrete dissipative structures. A generalized Ablowitz–Ladik (AL) equation with a cubic and quintic nonlinearity is then considered, and analysed via the full linear stability analysis of the nonlinear plane wave solution. We derive analytical expressions for the domain of existence as well as the gain of modulational instability of moving plane waves. In particular, we find that discreteness drastically modifies the stability condition as well as the quintic nonlinearity. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model. The generation of pulse trains with high repetition rate predicted by analytical study is then exhibited.

Considering a pulse-like ansatz, we derive different classes of exact soliton solutions of the modified complex Ginzburg–Landau equation. We then present the important variations which occur in the domain of stability of these solutions depending on the values of the renormalization coeffecients. This means that this term which can be considered for nonzero solutions and which does not generally occur in the literature could explain the lack of concordance between some theory and experiments.

The one-dimensional (1D) modified complex Ginzburg–Landau (MCGL) equation for travelling wave systems is analytically studied. We investigate soliton solutions of this equation and find solutions with fixed amplitude, arbitrary amplitude as well as chirp-free solitons. All these solutions are written in explicit form in terms of the parameters of the MCGL equation.

We investigate the general features of a ferroelectric D-dimensional hypercubic model, with a symmetric double Morse-type on-site potential and nearest-neighbour interaction, that exhibits structural phase transitions. The mean-field theory (MFT) is developed for this model where the anharmonicity is the main characteristic. It is based on making a Gaussian ansatz for the single-particle probability density function and helps us to make a more extensive survey of the order parameter. Two different cases are considered and analytical results analysed. Finally, we discuss the important features of the Hamiltonian, depending on the range of the force constant on the one hand and the strength of the anharmonicity on the other, which is responsible for these structural transitions (first order and second order).

We consider the stability of a continuous wave solution in line of vortices. The weakly nonlinear dynamics are governed by a one-dimensional (1D) discrete complex cubic Ginzburg–Landau (DCCGL) equation. In particular, within the framework of linear stability analysis, we show how the Lange and Newell criterion for the Benjamin–Feir instability is modified by the lattice effects as well as the second neighbour coupling. A noteworthy feature of the present study is that the initial condition is not disintegrated into trains of unstable patterns which have the shape of solitons in the absence of second neighbour couplings and quintic term. The simulations also show that the main observed physical signatures of this instability are a variety of propagative patterns for short-time scales and chaotic states for long-time scales where the linear perturbation analysis fails.

We investigate the features of a ferroelectric one-dimensional lattice model, with a class of symmetric deformable double-well substrate potentials and harmonic interaction, that exhibits structural phase transitions. The mean-field theory (MFT) is developed for this model, whose substrate potential shape varies in several manners as a function of a shape parameter. The temperature dependence of the structural order parameter is studied over a large temperature interval and then, the behavior of structural phase transitions is modified by the influence of quantum fluctuations and the shape parameter µ, particularly at low temperatures. Its effect on the phase diagram of temperature versus shape parameter is described and leads to highly nonlinear phase boundaries Tc(µ) in (Tc, µ) space. Also, the general phase diagram characteristics are derived from the order parameter saturation, leading to a more extensive survey of the order parameter, which is responsible for the structural transitions, and which becomes temperature independent below a saturation temperature θs. An application of the model to KH2PO4-type crystals and comparison of the model calculations with the experimental critical temperatures for KH2PO4 (KDP) and KD2PO4 (DKDP) yield satisfactory agreement. In the small-values limit, an approximate general Landau-type expression for the Gibbs free energy is given including the effects of order parameter saturation and which leads to the study of a tricrital phase transition and displacive limit case.

A revised Hamiltonian of a one-dimensional (ID) easy-plane ferromagnet in which the dipole–dipole and biquadratic exchange interactions are taken into account in addition to the Zeeman energy, the uniaxial anisotropy and the exchange energy, is proposed. Using a classical approximation, in the continuum limit, we show that in certain ranges of coupling constants, domain-walls in such a ferromagnet can be approximated by the perturbed sine Gordon (s.G) equation. In the case of weakly dipolar coupling, an analysis of the general properties of the soliton's motion as well as its modified profile are examined within the context of the perturbation theory. From a Ginzburg-Landau expansion of the free energy, it comes that one of the dipolar effects is to increase the stability of the sG solitons. The soliton contribution to the specific heat at low temperatures is obtained. We also investigated the transport properties in materials such as CsNiF3.

Wave modulations in the mono-inductance transmission line are studied by the use of a perturbation method. Far from the marginal state, that is for wavenumbers k larger than a critical wavenumber kc the evolution of a wave packet is described by the nonlinear Schrodinger (NLS) equation. Near this critical state of instability, it has been shown the NLS equation is not appropriate. We demonstrated that, in such regime, wave propagations are governed by a modified form of the NLS equation that involves higher-order nonlinearities. The associated revised modulational instability criterion is obtained and corresponding exact solutions are presented.

We use the soliton concept to derive analytical formulas of the mobility and diffusion coefficient of adsorbates in metallic substrates with the Peyrard-Remoissenet deformable potential. Our numerical values are compared to experimental results. The dependence of the diffusion coefficient on the deformability parameter can explain the gaps observed on existing measurements. A direct numerical simulation is carried out in view of measuring the mobility as the electric field and the deformability parameter vary.

We consider a nonlinear bi-inductance electrical transmission line which simulates a diatomic chain with non-linear cubic interactions. The linear spectrum of this model exhibits a gap which is proportional to the linear inductance difference. We analyse theoretically and numerically the coupled nonlinear excitations of such a bi-inductance line, which have a similar origin as the well-known gap solitons (GS) appearing in nonlinear systems with a spatial periodicity. Otherwise, these nonlinear modes are found in terms of asymmetric GS (kinks type) and are long-lived non-linear excitations.

Gap Solitons (GS) are found in a model of non-linear transmission lines which simulates a Toda lattice. These gap solitons are asymmetric kinks which can propagate on a long distance without drastic shape distortions, and therefore are long-lived non-linear excitations of the LC Toda lattice.

We present dynamical theory of soliton excitations in nonlinear coupled incommensurate chains which consists of two deformable chains of different atomic species, each with its own chemical potential, on the same substrate. In the continuum approximation, the motion equations are a set of coupled Sine-Gordon equations. The soliton solutions of these coupled equations are studied in detail. It has been shown that the frequency of the internal oscillations depends on the coupling parameter. The interaction energy between the two weakly coupled Sine-Gordon systems has been found. Results of the dynamical theory have been related to the transport properties in organic conductors such as TTF-TCNQ, KCP and others. Indeed, we have calculated some meaningful physical parameters of these compounds within the soliton limit, and discussed different types of behaviors shown at the transition with respect to variations of the physical parameters.

Physical systems concerned here are those in which the one dimensional Modified Complex Ginzburg–Landau equation or one of its derivative forms holds. By using this propagation equation, it is shown that the Lange and Newell's criterion for modulational instability of stokes waves can be recovered by performing the Stuart and Di Prima's method.

In the wake of the recent derivation of the new cubic nonlinear evolution equation of high-frequency pressure perturbations of a barothropic medium under relaxation (Kuetche V K et al 2014 J. Math. Phys. 55 052702), we closely investigate the head-on collisions of some typical localized waveguide excitations, which are solutions to the previous system. From the viewpoint of Hirotaʼs formalism, we delve into the structural scattering features of the interacting waves mentioned above. As a result, we find that there might exist some 'characteristic' amplitude ratio of the interacting waves at which the scattering changes its features. Accordingly, we provide an illustration of the previous result within the depiction of the interactions between three single soliton solutions alongside the phase-shift of each particle. Following these depictions, we address some physical implications of the results as well as the different potential applications.

We have numerically investigated the effects of helicity and inhomogeneities on DNA base pairs opening. The inhomogeneities are due to the site-dependent stacking and hydrogen bonding energies in DNA and protein molecules. We have considered a situation in which the active site of the RNA-polymerase molecule binds onto the promoter site of the spin-like model of the DNA molecule at the physiological temperature and creates a bubble. During the study, we have found that the helical coupling has to be very weak compared to intra-strand coupling in the real DNA molecule. Results show that inhomogeneities do not affect the general pattern of base pair opening, even as the periodic inhomogeneity introduces a train of periodic oscillations on the tail of the bubble; while the height of the bubble is an increasing function of the helical coupling parameter. The basic properties of breather-like modes, obtained here by taking into account helical structure and inhomogeneities, are essential for DNA functioning since such breathing-like modes are considered to be much better candidates for the nonlinear modes responsible for a locally open state where biological functioning takes place.

In this paper, we present a bifurcation and chaos analysis of a magnetopiezoelastic vibration energy harvester including inductance. We explain the behavior of these energy harvesters, particularly in the chaotic regime. We analyzed the model by using the Melnikov method, bifurcation diagrams, Lyapunov exponents and spectral methods. We determined the conditions for the onset of transition to chaos. This allows us to bound the regions of control parameters where the system displays desired chaotic oscillations and thus characterize the maximal harvestable power for this particular architecture.

We investigate the behavior of traveling waves in a spatial domain with the homogeneous boundary conditions by using the one-dimensional cubic–quintic complex Ginzburg–Landau equation. We focus our work on the absolute and convective instabilities and determine the dynamical regimes that are observed. As a consequence in the convectively unstable regime, the waves ultimately decay at any fixed position. Only when the threshold for the absolute instability is exceeded, the wave patterns may be maintained against the dissipation at the boundary. Consequently, coherent structures may be observed in the last case. We build a new state of phase diagram in the parameter plane spanned by the criticality parameter and the quintic nonlinear coefficient.

The modulational perturbations of the amplitude and phase for the time evolution of plane waves are studied in the semiquantum approach. Beyond the stability criterion from the nonlinear Schrodinger equation, there arise signatures of chaos in the dynamics of the associated cubic–quartic effective potential. The extended classical system described by fluctuation variables, nonlinearly coupled to the average ones, undergoes time-dependent variational approximation and foresees rooms of surprising regularity in the instability zone and chaos within the stable region of the wave number. The question of modulational instability (MI) for physical systems exhibits semiquantum chaotic features numerically observed with standard indicators. A dynamical quantum MI criterion is derived to resize the regions for stability with the correspondent momentum.

We apply a method based on the identification of coefficients of hyperbolic functions for the construction of the soliton solutions of the cubic and quintic nonlinear Ginzburg–Landau equations. This effective method improves the solution when the nonlinearity increases.

Random fluctuations in electronic density can considerably influence the profile of the resonance and stability curves of a column plasma. The fluctuations affect the resonance in different ways depending on the order of the considered resonance. The purpose of this effort is to investigate the effects of bounded noise on the primary resonances of density fluctuation in plasma. Along these lines, the response and stability are considered and analyzed using both the method of multiple scales and stochastic averaging. Further, we unveil very interesting dynamic responses in the frequency response. The statistical moment is calculated and its stability condition established. Through numerical simulations, we show that the density perturbation may undergo hysteretic transitions induced by external noisy excitation. The response of the global system is affected by bounded noise as demonstrated through the Poincare map.

Based on the nonlinear Helmholtz equation, we consider a model of the propagation of non-paraxial optical solitons, namely the non-paraxial nonlinear Schr?dinger equation. Using this model, we present a theoretical treatment leading to dynamical equations of motion by means of the collective variable (CV) approach. We show that the non-paraxiality parameter leads to a more complicated analysis of the dynamics of the relevant parameters, called CVs, associated with the soliton in comparison with those behaviors taking into account the approximation of the slowly varying amplitude of the propagating beam. We provide some propagation results of the analysis on a typical semi-infinite Kerr medium for some coefficient values of the model. Also, we find that stable propagation of non-paraxial solitons can be achieved for an appropriate choice of parameters.

The remarkable dynamics of waves propagating along the DNA molecule is described by the coupled nonlinear Schr?dinger equations. We consider both the single and the coupled nonlinear excitation modes and, under numerical simulations of the Peyrard?Bishop model, with the use of realistic values of parameters, their biological implications are studied. Furthermore, the characteristics of the coupled mode solution are discussed and we show that such a solution can describe the local opening observed within the transcription and the replication phenomena.

The purpose of this paper is to extend the application of the modified, generalized, rational harmonic balance method to the determination of approximate analytical solutions to general single-degree-of-freedom oscillator equations. We propose a simple form of rational periodic function that depends on a parameter r such that 0r

We study the nonlinear dynamics of the DNA double-helical chain using the Peyrard–Bishop–Dauxois (PBD) model. By using the Fourier series approach, we have found that the DNA dynamics in this case is governed by the modified discrete nonlinear Schrodinger (MDNLS) equation. Through the Jacobian elliptic function method, we investigate a set of exact solutions of this model. These solutions include the Jacobian periodic solution as well as bubble solitons. The stability of these solutions is also studied.