Integrability structures of the generalized Hunter--Saxton equation
Exactly Solvable and Integrable Systems
2020-12-15 v1
Abstract
We consider integrability structures of the generalized Hunter--Saxton equation. In particular, we obtain the Lax representation with nonremovable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give an example of employing the higher order symmetry to constructing exact globally defined solutions for the generalized Hunter--Saxton equation.
Cite
@article{arxiv.2012.06905,
title = {Integrability structures of the generalized Hunter--Saxton equation},
author = {Oleg I. Morozov},
journal= {arXiv preprint arXiv:2012.06905},
year = {2020}
}