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By using stochastic modeling, the investigation of the energy and wave characteristics of novel structures that develop in the sea and ocean currents becomes one of the most important advancements in the generation of sustainable and renewable energy. Theoretical examinations of random nonlinear Kundu–Mukherjee–Naskar (RNKMN) structures have become recommended in a random mode. The two-dimensional RNKMN equation permits exact and solved solutions that give rise to solitonic structures with adaptable properties. The obtained stochastic waves, under the influence of random water currents, represent a dynamically controlled system. It has been demonstrated that the stochastic parameter modulates wave forcing and produces energy wave collapse accompanied by medium turbulence. The fundamental wave characteristics establish an exact pattern for describing sea and ocean waves. [ABSTRACT FROM AUTHOR]

The exact solutions of the nonlinear Schrödinger equation (NLSE) predict consistent novel applicable existences such as solitonic localized structures, rouge forms, and shocks that rely on physical phenomena to propagate. Theoretical explanations of randomly nonlinear new extension NLSE structure solutions have undergone stochastic mode examination. This equation enables accurate and efficient solutions capable of simulating developed solitonic structures with dynamic features. The generated random waves are a dynamically regulated system that are influenced by random water currents behaviour. It has been noticed that the stochastic parameter modulates the wave force and supplies the wave collapsing energy with related medium turbulence. It has been observed that noise effects can alter wave characteristics, which may lead to innovative astrophysics, physical density, and ocean waves. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonlinear Chiral Schrödinger equation (CNLSE) in two dimensions where noise term affected randomly with time. This equation characterized some edges states of fractional-Hall Effect features in quantum. The CNLSE with multiplicative noise effects is studied as dynamical system to specify the acceptable solution types and then solved by unified solver method. The presented solutions are periodic envelopes, explosive, dissipative, symmetric solitons, and blow up waves. It was confirmed that the noise factor is dominant on all the wave conversion, growing and damping of envelopes and shocks. The presented technique in this study can be easily utilized for other nonlinear equations in applied science. Mathematics Subject Classification (2010) : 35C08, 65C20, 60H15, 35Q40, 35Q55, 35Q62 [ABSTRACT FROM AUTHOR]

The nonlinearly stochastic Schrödinger equation (NLSSE) predicts the nonlinear process that produces the waves decay in many physics applications. The unified method has been used in obtaining different new stochastic forms for NLSSE damped by noises in Itô sense. The derived structures appear in the form of rational, solitons, soliton-like shocks, and explosive propagations. The new stochastic solutions investigated the change of frequencies by noise term in NLSSE in nonlinear process that may be produced in many nonlinear wave applications. Finally, wave picture properties may controlled by noise term in Itô sense effect, which gives new information's for NLSSE in physics applications which is believed to be affected by the influence of Brownian motion that change the shape and structures of the generated decaying and damping waves. [ABSTRACT FROM AUTHOR]

A spline is a sufficiently smooth piecewise curve. B-spline functions are powerful tools for obtaining computational outcomes. They have also been utilized in computer graphics and computer-aided design due to their flexibility, smoothness and accuracy. In this paper, a numerical procedure dependent on the cubic B-spline (CuBS) for the time fractional diffusion wave equation (TFDWE) is proposed. The standard finite difference (FD) approach is utilized to discretize the Atangana–Baleanu fractional derivative (ABFD), while the derivatives in space are approximated through the CuBS with a θ -weighted technique. The stability of the propounded algorithm is analyzed and proved to be unconditionally stable. The convergence analysis is also studied, and it is of the order O (h 2 + (Δ t) 2) . Numerical solutions attained by the CuBS scheme support the theoretical solutions. The B-spline technique gives us better results as compared to other numerical techniques. [ABSTRACT FROM AUTHOR]

The collision of dressed dust acoustic solitons (DDASs) and the analytical higher-order phase shift are studied in a dusty plasma system that contains cold negative and positive dusty fluids and Maxwellian distributed for ions as well as electrons. The extended Poincaré–Lighthill–Kuo method is applied in order to obtain the nonlinear Korteweg–de Vries and phase shift equations, which admit the variation in soliton profiles and trajectories, respectively. Influences of the higher-order correction and the plasma fluid parameters such as charged dust grains concentration, negative-to-positive dust grain mass ratio, ion-to-negative dust grain number density ratio, and ion-to-electron temperature ratio on the characteristics of DDASs and their phase shifts are discussed. The comparisons between first- and higher-order contributions in rarefactive and compressive profiles are also taken into account. Furthermore, the present consideration may be utilised to mesosphere and magnetosphere. [ABSTRACT FROM AUTHOR]

Electrostatic nonlinear random Langmuir structures have been propagated in stochastic magnetospheres, clouds and solar wind. A theoretical description of Langmuir waves can be modeled by Schrödinger and Zakharov models with stochastic terms. It was explained that the stochastic parameter affects the forcing, collapsing in strongly density turbulence and density crystalline structures. The unified method has been implemented to provide new stochastic solutions for a Zakharov system in subsonic limit with noises via the Itô sense. This unified approach provides a variety of advantages, such as avoiding difficult calculations and explicitly providing pivotal solutions. It is easy to use, efficient, and precise. The induced generated energy during the collapsing of solar Langmuir wave bursts and clouds is determined by the solitonic formations. In addition, the collapsing strong turbulence or forcing density crystalline structures depend mainly on stochastic processes. Furthermore, electrostatic waves in clouds that may collapse are represented sometimes as dissipative shapes. So, the results of this investigation could be applicable to observations of energy seeding and collapsing in clouds. This energy is based on the electrostatic field and its related densities' perturbation in subsonic limits. Finally, it has been explored how noise parameters in the Itô sense affect the solar wind Langmuir waves' properties. So, the findings of this discussion may be applicable to real observations of energy collapsing and seeding in clouds. [ABSTRACT FROM AUTHOR]

The second order Burger's equation model is used to study the turbulent fluids, suspensions, shock waves, and the propagation of shallow water waves. In the present research, we investigate a numerical solution to the time fractional coupled-Burgers equation (TFCBE) using Crank–Nicolson and the cubic B-spline (CBS) approaches. The time derivative is addressed using Caputo's formula, while the CBS technique with the help of a θ -weighted scheme is utilized to discretize the first- and second-order spatial derivatives. The quasi-linearization technique is used to linearize the non-linear terms. The suggested scheme demonstrates unconditionally stable. Some numerical tests are utilized to evaluate the accuracy and feasibility of the current technique. [ABSTRACT FROM AUTHOR]

The KdV—Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged nonthermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space—time fractional KdV—Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated. [ABSTRACT FROM AUTHOR]

In this paper, a homogeneous system of unmagnetized collisionless plasma consisting of a cold electron fluid, low-temperature ion obeying Boltzmann-type distribution and high-temperature ion obeying non-thermal distribution is considered. The perturbation method with two different forms of stretching will be considered to drive the KdV and modified KdV (mKdV) equations. The Agrawal's method is applied to formulate the time-fractional KdV and mKdV equations. A variational iteration method is used to solve these equations. The results show that the fractional order of the differential equations can be used to modify the shape of the solitary pulse instead of adding higher order dissipation terms to the equations. This study may be useful to construct the compressive and rarefactive electrostatic potential pulses associated with the broadband electrostatic noise type emissions. [ABSTRACT FROM PUBLISHER]

Abstract: Collisionless unmagnetized plasma consisting of a mixture of warm ion-fluid and isothermal-electron is considered, assuming that the ion flow velocity has a weak relativistic effect. The reductive perturbation method has been employed to derive the Korteweg–de Vries (KdV) equation for small – but finite-amplitude electrostatic ion-acoustic waves in this plasma. The semi-inverse method and Agrawal’s method lead to the Euler–Lagrange equation that leads to the time fractional KdV equation. The variational-iteration method given by He is used to solve the derived time fractional KdV equation. The calculations show that the fractional order may play the same rule of higher order dissipation in KdV equation to modulate the soliton wave amplitude in the plasma system. The results of the present investigation may be applicable to some plasma environments, such as space-plasmas, laser-plasma interaction, plasma sheet boundary layer of the earth’s magnetosphere, solar atmosphere and interplanetary space. [Copyright &y& Elsevier]