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Damped-driven KdV and effective equations for long-time behaviour of its solutions. (English) Zbl 1231.35205

The author considers a sort of damped-driven KdV equation, and studies the limiting long-time behaviour of the KdV integrals of motion along a solution to the considered damped-driven KdV equation. The obtained limit is represented by a system of so-called effective equations for the damped-driven KdV equation, which are quasilinear stochastic heat equations with non-local nonlinearity.
Reviewer: Ma Wen-Xiu (Tampa)

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
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