Dark solitons of the Qiao's hierarchy

TL;DR

This paper derives a class of dark soliton solutions for Qiao's integrable hierarchy, expanding understanding of its soliton dynamics with solutions that approach constant values at infinity.

Contribution

It introduces explicit dark soliton solutions for Qiao's hierarchy, a novel class within this integrable system.

Findings

Derived explicit dark soliton solutions

Solutions are real functions with specific asymptotic behavior

Enhances understanding of Qiao's hierarchy dynamics

Abstract

We obtain a class of soliton solutions of the integrable hierarchy which has been put forward in a series of works by Z. Qiao. The soliton solutions are in the class of real functions approaching constant value fast enough at infinity, the so-called 'dark solitons'.