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On the compactness of the support of solutions of dispersive equations. (English) Zbl 0882.35106
The author disproves the existence of sufficiently smooth solutions, having the compact support on a nontrivial time interval, for a generalized KdV-type equation. The proof is based on the idea that the Fourier transform of a compactly supported function extends to an entire function of exponential type.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
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