English

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

Analysis of PDEs 2012-01-04 v1

Abstract

The dynamics of the poles of the two--soliton solutions of the modified Korteweg--de Vries equation ut+6u2ux+uxxx=0 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 <x<-\infty < x < \infty, exponentially decreasing to zero as x|x| \to \infty, that blow up in finite time.

Keywords

Cite

@article{arxiv.1201.0442,
  title  = {Singularity formation and blowup of complex-valued solutions of the modified KdV equation},
  author = {Jerry L. Bona and Stéphane Vento and Fred B. Weissler},
  journal= {arXiv preprint arXiv:1201.0442},
  year   = {2012}
}