Three Dimensional Reductions of Four-Dimensional Quasilinear Systems
Exactly Solvable and Integrable Systems
2017-12-06 v1
Abstract
In this paper we show that integrable four dimensional linearly degenerate equations of second order possess infinitely many three dimensional hydrodynamic reductions. Furthermore, they are equipped infinitely many conservation laws and higher commuting flows. We show that the dispersionless limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking Soliton equations introduced by O.I. Bogoyavlenski) are one and two component reductions (respectively) of one of these four dimensional linearly degenerate equations.
Keywords
Cite
@article{arxiv.1607.08442,
title = {Three Dimensional Reductions of Four-Dimensional Quasilinear Systems},
author = {Maxim V. Pavlov and Nikola M. Stoilov},
journal= {arXiv preprint arXiv:1607.08442},
year = {2017}
}