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arXiv · 2212.10130

Solutions to the wave equation for commuting flows of dispersionless PDEs

Natale Manganaro·Alessandra Rizzo·Pierandrea Vergallo
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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.

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Natale Manganaro, Alessandra Rizzo, Pierandrea Vergallo. 2022-12-20. Solutions to the wave equation for commuting flows of dispersionless PDEs. https://doi.org/10.1016/j.ijnonlinmec.2023.104611

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