On Kaup-Kupershchmidt type equations and their soliton solutions
Exactly Solvable and Integrable Systems
2017-03-20 v1
Abstract
We start with the Lax representation for the Kaup-Kupersschmidt equation (KKE). We We outline the deep relation between the scalar Lax operator and the matrix Lax operators related to Kac-Moody algebras. Then we derive the MKdV equations gauge equivalent to the KKE. Next we outline the symmetry and the spectral properties of the relevant Lax operator. Using the dressing Zakharov-Shabat method we demonstrate that the MKdV and KKE have two types of one-soliton solutions and briefly comment on their properties.
Keywords
Cite
@article{arxiv.1703.05850,
title = {On Kaup-Kupershchmidt type equations and their soliton solutions},
author = {Vladimir S. Gerdjikov},
journal= {arXiv preprint arXiv:1703.05850},
year = {2017}
}
Comments
19 pages, 1 figure