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On additional motion invariants of classical Hamiltonian wave systems. (English) Zbl 0651.35080
It is shown that the existence of an analytic invariant in addition to the natural ones (moment, energy and others) for a classical Hamiltonian wave system leads to the existence of infinitely many such invariants. However this phenomenon reduces a Hamiltonian system to a complete integrable system only if the dispersion law is non-degenerative. Results on degenerative dispersion laws and a factorizing of the S-matrix are presented. Concrete examples of Hamiltonian systems are adduced, for instance \(i\psi_ t-\psi_{xx}+\psi_{yy}=| \psi |^ 2\psi.\) Also the singular elements of the scattering matrix are considered.
Reviewer: V.A.Yumaguzhin

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35P25 Scattering theory for PDEs
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