Qualitative features of periodic solutions of KdV

Details Qualitative features of periodic solutions of KdV Qualitative features of periodic solutions of KdV

2011-10-03

arxiv.org/abs/1110.0455v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree.

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