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Deformations of bi-Hamiltonian structures of hydrodynamic type

โœ Scribed by Paolo Lorenzoni

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
315 KB
Volume
44
Category
Article
ISSN
0393-0440

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Separable Hamiltonians and integrable sy
Separable Hamiltonians and integrable systems of hydrodynamic type
โœ E.V. Ferapontov; A.P. Fordy ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 545 KB

We exhibit a surprising relationship between separable Hamiltonians and integrable, linearly degenerate systems of hydrodynamic type. This gives a new way of obtaining the general solution of the latter. Our formulae also lead to interesting canonical transformations between large classes of St~icke