The bi-Hamiltonian structure and new solutions of KdV6 equation

TL;DR

This paper establishes the bi-Hamiltonian structure of the KdV6 equation, demonstrates its equivalence to a deformed KdV equation with sources, and presents new soliton, positon, and negaton solutions.

Contribution

It introduces a bi-Hamiltonian formalism for KdV6 and provides new explicit solutions, advancing understanding of its integrable structure.

Findings

KdV6 is equivalent to RD-KdVESCS

Constructed bi-Hamiltonian formalism for KdV6

Presented new soliton, positon, and negaton solutions

Abstract

We show that the KdV6 equation recently studied in [1,2] is equivalent to the Rosochatius deformation of KdV equation with self-consistent sources (RD-KdVESCS) recently presented in [9]. The $t$-type bi-Hamiltonian formalism of KdV6 equation (RD-KdVESCS) is constructed by taking $x$ as evolution parameter. Some new solutions of KdV6 equation, such as soliton, positon and negaton solution, are presented.