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 $$u_t+6u^2{u}_x+u_{xxx}=0$$ are determined. A consequence of this study is the existence of classes of smooth, complex–valued solutions of this equation, defined for $-\mathrm{\infty }<x<\mathrm{\infty }$, exponentially decreasing to zero as $\mathrm{\mid }x\mathrm{\mid }\to \mathrm{\infty }$, that blow up in finite time.