Almost Periodicity in Time of Solutions of the Kdv Equation
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چکیده
We study the Cauchy problem for the KdV equation ∂tu−6u∂xu+∂ xu = 0 with almost periodic initial data u(x, 0) = V (x). We consider initial data V , for which the associated Schrödinger operator is absolutely continuous and has a spectrum that is not too thin in a sense we specify, and show the existence, uniqueness, and almost periodicity in time of solutions. This establishes a conjecture of Percy Deift for this class of initial data. The result is shown to apply to all small analytic quasiperiodic initial data with Diophantine frequency vector.
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تاریخ انتشار 2015