Conservation laws and Lax representation of Benney's long wave equations

Лебедев, Д. В.; Manin, Yu. I.

doi:10.1016/0375-9601(79)90756-4

Cited by 102 publications

(97 citation statements)

References 2 publications

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“…As shown by Manin and Lebedev in [7], the Benney hierarchy constructed in [5,6], is the zero-dispersion limit of the KP hierarchy (see, e.g., [2]). The Benney flow (1.2) is the quasiclassical limit of the second KP flow (g-scaled)…”

Section: Generalizationsmentioning

confidence: 94%

A Hidden Group Structure for the Integrals of the Benney System

Kupershmidt¹

2008

JNMP

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Section: Generalizationsmentioning

confidence: 94%

A Hidden Group Structure for the Integrals of the Benney System

Kupershmidt¹

2008

JNMP

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“…One of the advantages of this method is now obvious, namely, one can go to the Lax representation of the model in the dispersionless limit in a natural manner [13]. In fact, if we consider the limit κ → 0, in such a model, it leads to…”

Section: Basic Definitionsmentioning

confidence: 99%

Properties of Moyal–Lax representation

Das

Popowicz

2001

Physics Letters B

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The properties of standard and the nonstandard Moyal-Lax representations are systematically investigated. It is shown that the Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. We show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The Moyal-Lax description leads in a natural manner to the dispersionless limit and provides the second Hamiltonian structure of dispersionless integrable models, which has been an open question for sometime.

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“…Manin [5], and Lebedev and Manin [6]. We extend Manin' homogenous system (1.1) are in involution relative to the symplectlc structure introduced in this article.…”

Section: Introductionmentioning

confidence: 97%