Construction of solutions to the L2-critical KdV equation with a given asymptotic behaviour

Raphaël Côte

Type: Article

Publication Date: 2007-06-15

Citations: 33

DOI: https://doi.org/10.1215/s0012-7094-07-13835-3

Abstract

We consider the critical Korteweg–de Vries (KdV) equation: ut+(uxx+u5)x=0, t,x∈R. Let Rj(t,x)=Qcj(x−xj−cjt) (j=1,…,N) be N soliton solutions to this equation. Denote U(t) the KdV linear group, and let V∈H1 be with sufficient decay on the right; that is, let (1+x+2+δ0)V∈L2 be for some δ0>0. We construct a solution u(t) to the critical KdV equation such that limt→∞‖u(t)−U(t)V−∑j=1NRj(t)‖H1=0.

Locations

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