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

Author： Qiao Zhijun Li Jibin

Publisher： Edp Sciences

E-ISSN： 1286-4854|94|5|50003-50003

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.94, Iss.5, 2011-05, pp. : 50003-50003

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

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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