University of Cambridge > Talks.cam > Partial Differential Equations seminar > Finite time blowup of complex-valued solutions of the Korteweg-de Vries and the modified Korteweg-de Vries equations

Finite time blowup of complex-valued solutions of the Korteweg-de Vries and the modified Korteweg-de Vries equations

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We show that there exist complex-valued solutions of the KdV and mKdV equations which blow up in finite time. This is accomplished in the case of spatially periodic solutions on the line, as well as for solutions which decay to zero at infinity. In the former case, we give an argument encompassing a large class of solutions. In the latter case, we give an explicit construction based on the formulas for the “2-soliton” solutions.

This talk is part of the Partial Differential Equations seminar series.

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