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

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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