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. 
Jerry L. Bona (UIC), St\'ephane Vento (LAGA), Fred B. Weissler (LAGA)
math.AP