Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations
Exactly Solvable and Integrable Systems
2009-08-20 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.
Cite
@article{arxiv.0907.3205,
title = {Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations},
author = {V. G. Dubrovsky and A. V. Gramolin},
journal= {arXiv preprint arXiv:0907.3205},
year = {2009}
}
Comments
Talk given at the Workshop "Nonlinear Physics: Theory and Experiment. V", Gallipoli (Lecce, Italy), 12-21 June, 2008