On the nonlinear new wave solutions in unstable dispersive environments

Abstract

The exact new solutions are given in the form of rational, exponential, trigonometric and hyperbolic forms in which some of them are new and realistic for Schrödinger equation. Numeral studies have been reveals that the obtained solutions may be applicable for some physical environments, such as plasma fluids and fiber communications. The computational study and obtained conclusions reported that the offered methods are pretentious, robust and influential in applications of voyager storm analysis, observations of space plasmas and in optical fibers.

Solving nonlinear Schrodinger equation using stable implicit finite difference method in single‐mode optical fibers

“…Thomas algorithm enhanced the computational efficiencies of binary collisions and solitary solutions by using random perturbations to the initial conditions. 30 Many researches [3][4][5][6][7][8][9][10][11][12][13] tend to solve the NLSE equation by using different numerical and analytical methods with no focus on the parameters considered in Equation (1.1). Therefore, the main focus of this article is to solve the NLSE numerically by using an implicit finite difference method which is second order in space and time and unconditionally stable.…”

“…11 The unstable nonlinear new solitary characteristics in strong dispersive space and environmental fluids have been investigated to discuss the wave behavior at critical points that existed in the medium in periodic series. 13 Moreover, the NLSE performs a definitely main role in nonlinear applications and studies in fiber optics due to its possessing of soliton solutions. 1,2,[18][19][20][21] The sine-Gordon and generalized tanh techniques are introduced to obtain the solitary optical solutions to perturbed NLSE (PNLSE).…”

“…The temporal‐optical solitonic waves of the nonlinear Schrodinger equation (NLSE) have been investigated theoretically, experimentally, and by simulation to examine its properties in communications using fiber optics 3–13 . Also, these optical fibers are introduced as a serious alternative to next generations in ultrafast telecommunications systems 3,7,9,13 .…”

“…The temporal‐optical solitonic waves of the nonlinear Schrodinger equation (NLSE) have been investigated theoretically, experimentally, and by simulation to examine its properties in communications using fiber optics 3–13 . Also, these optical fibers are introduced as a serious alternative to next generations in ultrafast telecommunications systems 3,7,9,13 . The nonlinearly forms of NLSE became one of the major delegated ways for depicting the waves behavior in a large number of nonlinear physical applications, that is, plasmas, optics, fluids, deeper water, semiconductors, Bose–Einstein condensation, and dynamical models 3–17 .…”

Super electron acoustic propagations in critical plasma density

“…Recently, there is a huge development in analytical methods for getting solutions for NPDEs, see [24][25][26][27][28][29][30][31][32][33][34][35][36] and references therein. So, the aim of this work is to use one of these methods to introduce new solution forms applicable for auroral zone observations.…”