# American Institute of Mathematical Sciences

November  2013, 33(11&12): 4811-4840. doi: 10.3934/dcds.2013.33.4811

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

 1 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States 2 Université Paris 13, Sorbonne Paris Cité, CNRS UMR 7539 Laboratoire Analyse, Géométrie et Applications, 99 avenue J.B. Clément - 93430 Villetaneuse, France, France

Received  November 2011 Revised  August 2012 Published  May 2013

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 investigated. 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.
Citation: Jerry L. Bona, Stéphane Vento, Fred B. Weissler. Singularity formation and blowup of complex-valued solutions of the modified KdV equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4811-4840. doi: 10.3934/dcds.2013.33.4811
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