Hamiltonian form and infinitely many conservation laws for a quasilinear system

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Abstract

In the present paper we show the closed relation between the existence of smooth periodic solutions for a certain quasilinear system and the existence question for the integral of motion of a classical Hamiltonian system with 1.5 degrees of freedom. It turns out that this quasilinear system has infinitely many additional conservation laws and moreover can be written in the Hamiltonian form of the hydrodynamic type. There is the hope that these results will help to classify those classical Hamiltonian systems with 1.5 degrees of freedom which are completely integrable.

Original languageEnglish
Pages (from-to)925-930
Number of pages6
JournalNonlinearity
Volume10
Issue number4
DOIs
StatePublished - Jul 1997

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