In this paper we study the deformations of bi-Hamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion up to a certain order in the deformation parameter. This fact suggests that these systems could have, at least for small times, multi-soliton solutions. Our numerical experiments confirm this hypothesis
Lorenzoni, P. (2002). Deformations of bi-Hamiltonian structures of hydrodynamic type. JOURNAL OF GEOMETRY AND PHYSICS, 44(2-3), 331-375 [10.1016/S0393-0440(02)00080-3].
Deformations of bi-Hamiltonian structures of hydrodynamic type
Lorenzoni, P.
2002
Abstract
In this paper we study the deformations of bi-Hamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion up to a certain order in the deformation parameter. This fact suggests that these systems could have, at least for small times, multi-soliton solutions. Our numerical experiments confirm this hypothesis
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