New optical soliton solutions to the (n+1) dimensional time fractional order Sinh-Gordon equation

Abstract

This article studies and constructs new optical soliton solutions for the (n+1)-dimensional time fractional order Sinh-Gordon equation. First, we change the differential equation into Ordinary differential equation which is connected with a quartic polynomial based on traveling wave transformation. Then using the polynomial complete discrimination system to classify the roots of the fourth degree polynomial, the exact solutions of the Sinh-Gordon equation are classified, and these specific expressions of optical soliton solutions are given. This solution process is simple, fast, and very effective. The characteristics of some exact solutions were given using 3D, 2D, and contour graphs, which help researchers gain a deeper understanding of the physical characteristics corresponding to the model which we discuss in this article.