Solutions to the wave equation for commuting flows of dispersionless PDEs

被引：2
作者：
Manganaro, Natale [1 ]
Rizzo, Alessandra [1 ]
Vergallo, Pierandrea [2 ,3 ]
机构：
[1] Univ Messina, Dept Math Comp Phys & Earth Sci, Vle F Stagno Alcontres 31, I-98166 Messina, Italy
[2] Univ Milan, Dept Math F Enriques, Via C Saldini 50, I-20133 Milan, Italy
[3] Ist Nazl Fis Nucl, Sez Milano, Via Celoria 16, I-20133 Milan, Italy
来源：
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2024年 / 159卷
关键词：
Hamiltonian systems; Wave equation; Method of differential constraints; HYDRODYNAMIC TYPE; SYSTEMS;
D O I：
10.1016/j.ijnonlinmec.2023.104611
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
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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页数：7
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