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Pré-Publication, Document De Travail Année : 2012

Singularity formation and blowup of complex-valued solutions of the modified KdV equation

Résumé

The dynamics of the poles of the two--soliton solutions of the modified Korteweg--de Vries equation $$ u_t + 6u^2u_x + u_{xxx} = 0 $$ are determined. A consequence of this study is the existence of classes of smooth, complex--valued solutions of this equation, defined for $-\infty < x < \infty$, exponentially decreasing to zero as $|x| \to \infty$, that blow up in finite time.
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Dates et versions

hal-00655739 , version 1 (02-01-2012)

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Jerry L. Bona, Stéphane Vento, Fred B. Weissler. Singularity formation and blowup of complex-valued solutions of the modified KdV equation. 2012. ⟨hal-00655739⟩
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