Novel approximations to a nonplanar nonlinear Schrödinger equation and modeling nonplanar rogue waves/breathers in a complex plasma

Abstract

Studying the dynamics of several nonlinear structures that arise in nonlinear science including optical fiber and various plasma models in a nonplanar (cylindrical and spherical) geometry is closer to reality rather than the one-dimensional planar geometry. Motivated by this point and based on the laboratory results and satellite observations, thus, this work is performed to derive some novel general analytical approximations (including any nonplanar modulated structures like rogue waves (RWs), breathers, bright and dark envelope solitons, etc.) to a nonplanar nonlinear Schrödinger equation (nNLSE) using the ansatz method. Based on this method, two general formulas for the analytical approximations are derived. The most important characteristic of the obtained approximations is that they are general solutions that can be employed for studying any modulated nonplanar structures described by the nNLSE. The residual error formulas for the cylindrical and spherical rational solutions are derived and discussed numerically to verify the precision of the obtained approximations. Also, the nNLSE is analyzed numerically via the method of lines (MOLs). Moreover, a comparison between analytical and numerical approximations is carried out. As a real application to the obtained solutions, the propagation of nonplanar rational solutions including rogue waves (RWs) and breathers structures in a dusty plasma are investigated. The obtained approximations will quickly find acceptance in dealing with the bounded nonlinear phenomena in different plasma models and many other branches of science.