Nondegenerate solitons in the integrable fractional coupled Hirota equation

TL;DR

This paper derives explicit multi-soliton solutions for an integrable fractional coupled Hirota equation, revealing unique properties of nondegenerate fractional solitons and their superposition behavior.

Contribution

It introduces a new integrable fractional coupled Hirota equation and constructs its explicit multi-soliton solutions using inverse scattering, including nondegenerate fractional solitons.

Findings

Fractional two-solitons can be viewed as superpositions of single solitons at large times.

Explicit multi-soliton solutions are obtained via inverse scattering transformation.

Nondegenerate fractional solitons are identified under specific constraints.

Abstract

In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirota equation and give its explicit form. Unlike the previous nonlinear fractional equations, this type of nonlinear fractional equation is integrable. Therefore, we obtain the fractional $n$-soliton solutions of the fractional coupled Hirota equation by inverse scattering transformation in the reflectionless case. In particular, we analyze the one- and two-soliton solutions of the fractional coupled Hirota equation and prove that the fractional two-soliton can also be regarded as a linear superposition of two fractional single solitons as $|t|\to\infty$. Moreover, under some special constraint, we also obtain the nondegenerate fractional soliton solutions and give a simple analysis for them.