Solutions to the wave equation for commuting flows of dispersionless PDEs
Mathematical Physics
2023-12-15 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction procedure of differential constraints to obtain a complete set of solutions of such an equation for some fixed velocities a^2(u,v). As a result, we present some examples of Hamiltonian integrable systems (as the shallow water equations) with relative symmetries, conserved quantities and solutions.
Keywords
Cite
@article{arxiv.2212.10130,
title = {Solutions to the wave equation for commuting flows of dispersionless PDEs},
author = {Natale Manganaro and Alessandra Rizzo and Pierandrea Vergallo},
journal= {arXiv preprint arXiv:2212.10130},
year = {2023}
}