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Non-Noether symmetries in integrable models

George Chavchanidze

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In the present paper the non-Noether symmetries of the Toda model, nonlinear Schrödinger equation and Korteweg–de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in involution and lead to the bi-Hamiltonian realizations of the above-mentioned models.


PACS

02.30.Ik Integrable systems

03.65.Ge Solutions of wave equations: bound states

MSC

70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 6 (13 February 2004)

Received 27 August 2003

Published 28 January 2004



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