Optical wave solutions of highly dispersive nonlinear Schrödinger equation without the existence of inter-model dispersion

Abstract

Abstract This paper studies highly dispersive solitons with a nonlinear refractive index without inter-model dispersion, which is of great significance in long-distance optical soliton communication and therefore has important research value. By using the trial equation method and the complete discrimination system for the polynomial method, we get a large number of solutions that were not previously studied by scholars and divide these solutions into four modes: rational modes, solitary wave modes, triangular function periodic modes, and elliptic function double periodic modes. These solutions demonstrate the propagation mode and spatial structure of the equation. Compared with previous scholars’ research, the method used in this article is simpler, easier, and more effective to understand. Besides, two-dimensional images are provided.