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Statistical mechanics of nonlinear wave equations. (English. Russian original) Zbl 0929.35097

J. Math. Sci., New York 94, No. 4, 1630-1634 (1999); translation from Zap. Nauchn. Semin. POMI 235, 287-294 (1996).
Summary: The recurrences of initial states for nonlinear wave equations of the form \(\square Q+ f(Q)= 0\) with odd \(f\) are studied. The main result refines and generalizes the investigations of Friedlander and is related to the Poincaré theorem for finite-dimensional Hamiltonian systems.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
34C28 Complex behavior and chaotic systems of ordinary differential equations

Citations:

Zbl 0924.00015

References:

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