The Painlevé property, Bäcklund transformation, Lax pair and new analytic solutions of a generalized variable-coefficient KdV equation from fluids and plasmas

Author： Yuping Zhang Junyi Wang Guangmei Wei Ruiping Liu

Publisher： IOP Publishing

E-ISSN： 1402-4896|90|6|65203-65212

ISSN： 1402-4896

Source： Physica Scripta, Vol.90, Iss.6, 2015-06, pp. : 65203-65212

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

Previous Menu Next

Abstract

A generalized variable-coefficient Korteweg–de Vries (KdV) equation with variable-coefficients of x and t from fluids and plasmas is investigated in this paper. The explicit Painlevé-integrable conditions are given out by Painlevé test, and an auto-Bäcklund transformation is presented via the truncated Painlevé expansion. Under the integrable condition and auto-Bäcklund transformation, the analytic solutions are provided, including the soliton-like, periodic and rational solutions. Lax pair, Riccati-type auto-Bäcklund transformation (R-BT) and Wahlquist–Estabrook-type auto-Bäcklund transformation (WE-BT) are constructed in extended AKNS system. One-soliton-like and two-soliton-like solutions are obtained by R-BT and nonlinear superposition formula is obtained by WE-BT. The bilinear form and N-soliton-like solutions are presented by Bell-polynomial approach. Based on the obtained analytic solutions, the propagation characteristics of waves effected by the variable coefficients are discussed.