Abstract:Abstract. Consider a perturbed KdV equation:ut + uxxx − 6uux = ǫf (u(·)), x ∈ T = R/Z, T u(x, t)dx = 0, where the nonlinear perturbation defines analytic operators u(·) → f (u(·)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ǫ-quasiinvariant measure µ and satisfies some additional mild assumptions. Let u ǫ (t) be a solution. Then on time intervals of order ǫ −1 , as ǫ → 0, its actions I(u ǫ (t, ·)) can be approximated by solutions of a certain well-posed averaged equation, provided th… Show more
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