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Analyticity of solutions of the Korteweg-de Vries equation. (English) Zbl 0742.35056

Summary: It is proven that if the initial function of the Korteweg-de Vries equation is analytic and has an analytic continuation to a strip containing the real axis, then the local in time solution has the same property, although the width of the strip might decrease with time. The result contains the case of the complex-valued initial function.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B65 Smoothness and regularity of solutions to PDEs
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