English

Negative order KdV equation with both solitons and kink wave solutions

Mathematical Physics 2011-05-26 v3 math.MP Pattern Formation and Solitons Exactly Solvable and Integrable Systems Fluid Dynamics

Abstract

In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is (uxxu)t=2uux(\frac{-u_{xx}}{u})_{t}=2uu_{x}, which actually comes from the negative KdV hierarchy and could be transformed to the Camassa-Holm equation through a gauge transform. The Lax pair of the equation is derived to guarantee its integrability, and furthermore the equation is shown to have classical solitons, periodic soliton and kink solutions.

Keywords

Cite

@article{arxiv.1101.1605,
  title  = {Negative order KdV equation with both solitons and kink wave solutions},
  author = {Zhijun Qiao and Jibin Li},
  journal= {arXiv preprint arXiv:1101.1605},
  year   = {2011}
}