Solitons in media with mixed, high-order dispersion and cubic nonlinearity

TL;DR

This paper develops analytical solutions for bright solitons in media with high-order dispersion and cubic nonlinearity, expanding understanding beyond traditional quadratic dispersion models.

Contribution

It introduces explicit formulas for solitons at arbitrary dispersion orders and practical methods to derive their dispersion relations, advancing the study of higher order dispersion solitons.

Findings

Analytic expressions for solitons at any dispersion order

Methods to determine dispersion relations for these solitons

Framework for exploring solitons in high-order dispersion systems

Abstract

Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present analytic expressions for families of bright soliton solutions at arbitrary dispersion orders and practical methods to obtain the associated dispersion relations. These results provide a framework for considering higher order dispersion solitons and show the potential for further investigation of solitons in higher order dispersion systems.