Negative order KdV equation with both solitons and kink wave solutions

Details Negative order KdV equation with both solitons and kink wave solutions Negative order KdV equation with both solitons and kink wave solutions

2011-01-08

arxiv.org/abs/1101.1605v3

Europhys.Lett.94:50003,2011

Physics

Mathematical Physics

Scientific paper

10.1209/0295-5075/94/50003

In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is $(\frac{-u_{xx}}{u})_{t}=2uu_{x}$, 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.

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