Singularity Formation and Blowup of Complex-Valued Solutions of the Modified KDV Equation
Bona, Jerry L.
Weissler, Fred B.
PublisherAmerican Institute of Mathematical Sciences
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The dynamics of the poles of the two soliton solutions of the modified Korteweg-de Vries equation ut + 6u2ux + uxxx = 0 are investigated. A consequence of this study is the existence of classes of smooth, complex-valued solutions of this equation, defined for ∞1 < x < 1, exponentially decreasing to zero as x → ∞, that blow up in finite time.