Multiple rational rogue waves for higher dimensional nonlinear evolution equations via symbolic computation approach

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota-Satsuma-Ito(HSI)equation and the newly proposed extended(3+1)-dimensional Jimbo-Miwa(JM)equation with the help of a symbolic computation technique.By incorporating a direct variable trans-formation and utilizing Hirota’s bilinear form,multiple rogue wave structures of different orders are ob-tained for both generalized HSI and JM equation.The obtained bilinear forms of the proposed equations successfully investigate the 1st,2nd and 3rd-order rogue waves.The constructed solutions are verified by inserting them into original equations.The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves.Physical properties of these waves are governed by different parameters that are discussed in details.

Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

This paper investigates the perturbed Boussinesq equation that emerges in shallow water waves.The perturbed Boussinesq equation describes the properties of longitudinal waves in bars,long water waves,plasma waves,quantum mechanics,acoustic waves,nonlinear optics,and other phenomena.As a result,the governing model has significant importance in its own right.The singular manifold method and the unified methods are employed in the proposed model for extracting hyperbolic,trigonometric,and rational function solutions.These solutions may be useful in determining the underlying context of the physical incidents.It is worth noting that the executed methods are skilled and effective for examining nonlinear evaluation equations,compatible with computer algebra,and provide a wide range of wave solutions.In addition to this,the Painlevétest is also used to check the integrability of the governing model.Two-dimensional and threedimensional plots are made to illustrate the physical behavior of the newly obtained exact solutions.This makes the study of exact solutions to other nonlinear evaluation equations using the singular manifold method and unified technique prospective and deserving of further study.

Optical solitons for the decoupled nonlinear Schr?dinger equation using Jacobi elliptic approach

Most of the important aspects of soliton propagation through optical fibers for transcontinental and transoceanic long distances can best be described using the nonlinear Schr?dinger equation.Optical solitons are electromagnetic waves that span in nonlinear dispersive media and permit the stress and intensity to stay unaltered as a result of the delicate balance between dispersion and nonlinearity effects.However,this study exploited the Jacobi elliptic method and obtained different soliton solutions of the decoupled nonlinear Schr?dinger equation with ease.Discussions about the obtained solutions were made with the aid of some 3D graphs.

Fractional soliton dynamics of electrical microtubule transmission line model with local M-derivative

In this paper,two integrating strategies namely exp[-Ф(Х)]and (G'/G^(2))-expansion methods together with the attributes of local-M derivatives have been acknowledged on the electrical microtubule(MT)model to retrieve soliton solutions.The said model performs a significant role in illustrating the waves propagation in nonlinear systems.MTs are also highly productive in signaling,cell motility,and intracellular transport.The proposed algorithms yielded solutions of bright,dark,singular,and combo fractional soliton type.The significance of the fractional parameters of the fetched results is explained and presented vividly.