Smooth soliton solutions of a new integrable equation by Qiao

TL;DR

This paper establishes a transformation linking a new integrable equation to the mKdV equation, enabling derivation of smooth soliton solutions from known solutions of the mKdV.

Contribution

It introduces a transformation that connects the new equation with the mKdV, allowing the construction of smooth soliton solutions for the new integrable equation.

Findings

Derived smooth soliton solutions for the new equation.

Established a transformation relating the new equation to the mKdV.

Demonstrated the method's effectiveness in solution construction.

Abstract

We find a transformation which relates a new third-order integrable nonlinear evolution equation, introduced recently by Qiao, with the well-known modified Korteweg - de Vries equation. Then we use this transformation to derive smooth soliton solutions of the new equation from the known rational and soliton solutions of the old one.