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

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  • 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 $ - oo \lt x \lt oo $, exponentially decreasing to zero as $|x| \to oo$, that blow up in finite time.

    Mathematics Subject Classification: 35Q53, 35Q51, 37K40, 35A21, 35B44.


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