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The local ill-posedness of the modified KdV equation. (English) Zbl 0858.35130
Summary: We find a new method for proving the local ill-posedness of the Cauchy problem for nonlinear partial differential equations. The method is used to prove that the Cauchy problem for the modified KdV equation is ill-posed in Sobolev spaces \(H^s(\mathbb{R})\), \(s<-1/2\).

35R25 Ill-posed problems for PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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