Negative order KdV equation with both solitons and kink wave solutions

Abstract

In this paper, we report an interesting integrable equation that has both solitons and kink solutions. The integrable equation we study is $(\frac{-u_{xx}}{u}{)}_t=2u{u}_x$, 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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Cited by in corpus (3)

• Generalized negative flows in hierarchies of integrable evolution equations
• A study of two new generalized negative KdV type equations
• Exact solutions of time fractional generalized Burgers-Fisher Equation using generalized Kudryashov method