Bifurcation of traveling wave solutions of the perturbed nonlinear Schrödinger equation

Abstract

Abstract In this paper, the traveling wave solutions of perturbed nonlinear Schrödinger equation in nanofibers are studied by using the bifurcation theory of dynamic systems. The phase portrait and orbit analysis of perturbed nonlinear Schrödinger equation are given in the form of graph, and the traveling wave solutions corresponding to perturbed nonlinear Schrödinger equation under different conditions are derived and analyzed. Moreover, periodic wave solutions and periodic singular wave solutions are obtained by using Jacobian elliptic function on the basis of predecessors. And it was found that the limit of periodic wave solutions is solitary wave solutions. The limit of periodic singular wave solutions is singular wave solutions. These results provide convenience for scholars to study the physical value of this equation and allow for a deeper understanding of nonlinear phenomena and their physical essence in nanofibers.