Disturbance solutions for the long–short-wave interaction system using bi-random Riccati–Bernoulli sub-ODE method

Abstract

This article applied the Riccati-Bernoulli (RB) sub-ODE method in order to get new exact solutions for the long-short-wave interaction (LS) equations. Namely, we obtain deterministic and random solutions, since we consider the proposed method in deterministic and random cases. The RB sub-ODE technique gives the travelling wave solutions in forms of hyperbolic, trigonometric and rational functions. It is shown that the proposed method gives a robust mathematical tool for solving nonlinear wave equations in applied science. Furthermore, some bi-random variables and some random distributions are used in random case corresponding to the LS system. The stability for the obtained solutions in random case is considered. In addition, there is a display of several numerical simulations, which helps to understand the physical phenomena of these soliton wave solutions. ARTICLE HISTORY

Some new chiral and perturbed chiral solitary waves in quantum Hall effect

“…6–12 Due to the nonlinear Schrödinger equation’s (NLSE’s) rich physical features, optical solutions, namely, complex and hyperbolic solitons, are now the most interesting fields of nonlinear wave propagation in plasma of fluids, electromagnetic wave propagation, deep water, quantum mechanics, superconductivity, electromagnetic wave propagation, nuclear physics, and magneto-static spin waves optical fibers communications. 13–21 Various physicists and mathematicians proposed and developed some standing wave stabilities for NLSEs and related equations such as perturbed, Hartree, Choquard, and its fractional form equations. 22–27…”

“…[6][7][8][9][10][11][12] Due to the nonlinear Schrödinger equation's (NLSE's) rich physical features, optical solutions, namely, complex and hyperbolic solitons, are now the most interesting fields of nonlinear wave propagation in plasma of fluids, electromagnetic wave propagation, deep water, quantum mechanics, superconductivity, electromagnetic wave propagation, nuclear physics, and magneto-static spin waves optical fibers communications. [13][14][15][16][17][18][19][20][21] Various physicists and mathematicians proposed and developed some standing wave stabilities for NLSEs and related equations such as perturbed, Hartree, Choquard, and its fractional form equations. [22][23][24][25][26][27] The concept of chiral solitons represents a crucial role in the developments of quantum mechanics, specifically, in the field of quantum Hall effect (QHE) and biological sciences in the context of neurosciences, where the appearance of chiral solitons is known to appear.…”

The noise sense effects on the characteristic nonlinearly Schrödinger equation solitary propagations

“…17 Many authors studied physical problems that described by deterministic and stochastic nonlinear equations. [21][22][23][24][25] Alharbi et al investigated the spatiotemporal dispersion effects using resonant SNEs using statistical beta distribution. 22 Many phenomena's in nature were described by different forms of differential equations (DEs) and NPDEs.…”

“…[43][44][45][46] The impact of decay cussed by stochastic term in NPDEs is very serious to illustrate the damping phenomena in numerous nature issues in fluid mechanics, chemical engineering, biological systems, fluids, and physics of solid state. [21][22][23]47 In this work, the NLSSE has been solved by unified solver to obtain stochastic rational, trigonometric, and hyperbolic solutions when noise in Itô sense is present. This solver produces these families of solutions via free physical parameters.…”

Effects of Brownian noise strength on new chiral solitary structures

“…[1][2][3][4][5][6][7][8] Recently, the nonlinear stochastic partial differential equations (NSPDEs) have been extensively studied by many scientists due to the fact that these equations are successfully utilized for modeling various physical phenomena such as superfluid, HIV internal virus dynamics, telecommunications, astrophysical dynamics, and growth of biological populations. [9][10][11][12][13][14] These equations often rely on a noise source such as a white noise and certain probability laws. [15][16][17][18] The investigation of optical solitons for the NSPDEs is an important topic as explained in.…”