Generalized flat-top soliton solutions to the nonlinear Schrödinger equation with multi power-law nonlinearities and higher-order dispersion terms

Abstract

We consider a generalized nonlinear Schrödinger equation with multi-power-law nonlinearities and higher-order dispersion terms. Employing two modified analytical solution methods, namely, the separation of variables and exp-expansion methods, we systematically derive a broad spectrum of exact solutions. The obtained solutions encompass a variety of classes, including solitonic-like, trigonometric-like, and rational forms. Utilizing the separation of variables method, we derive a new form of the flat-top soliton solution to the nonlinear Schrödinger equation with cubic-quintic nonlinearity, in addition to other new solutions. Using the exp-expansion method, we present, for the first time, families of generalized flat-top soliton solutions to the nonlinear Schrödinger equation with arbitrary dual-power-law nonlinearity. Exponential-type and algebraic-type families of flat-top solutions were particularly obtained. In addition, new solutions to the nonlinear Schrödinger equation with higher-order dispersion and higher-power-law nonlinearities are derived. The new solutions were shown to be stable according to the Vakhitov-Kolokolov criterion.

Keywords: Generalized nonlinear Schrödinger equation, Multi power‑law nonlinearity, Higher‑order dispersion, Flat‑top soliton, Separation of variables method