Auto-Bäcklund Transformation, Lax Pairs and Painlevé Property of $u_t+p(t)uu_x+q(t)u_{xxx}+r(t)u=0$

R. Asokan

Abstract


Using the Painlevé property (PP) of partial differential equations, the auto-Bäcklund transformation (ABT) and Lax pairs for Korteweg-de Vries (KdV) equation with time-dependent coefficients are obtained. The Lax pair criterion also makes it possible for some new models of the variable coefficient KdV equation to be found that can represent nonsoliton dynamical systems. This can explain the wave breaking phenomenon in variable depth shallow water.

Keywords


Korteweg-de Vries (KdV) equation; Painlevé property; Resonances; Exact solutions; Auto-Bäcklund transformation and Lax pairs

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DOI: http://dx.doi.org/10.26713%2Fjims.v4i1.72

eISSN 0975-5748; pISSN 0974-875X