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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >The Painleve property, Backlund transformation, Lax pair and new analytic solutions of a generalized variable-coefficient KdV equation from fluids and plasmas
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The Painleve property, Backlund transformation, Lax pair and new analytic solutions of a generalized variable-coefficient KdV equation from fluids and plasmas

机译：流体和等离子体的广义变系数KdV方程的Painleve性质，Backlund变换，Lax对和新的解析解

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摘要

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 Painleve-integrable conditions are given out by Painleve test, and an auto-Backlund transformation is presented via the truncated Painleve expansion. Under the integrable condition and auto-Backlund transformation, the analytic solutions are provided, including the soliton-like, periodic and rational solutions. Lax pair, Riccati-type auto-Backlund transformation (R-BT) and Wahlquist-Estabrook-type auto-Backlund 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.
机译：本文研究了广义的变系数Korteweg-de Vries（KdV）方程，该方程具有来自流体和等离子体的x和t的变系数。通过Painleve检验给出了明确的Painleve可积条件，并通过截短的Painleve展开给出了自动Backlund变换。在可积条件和自动Backlund变换下，提供了解析解，包括类孤子，周期和有理解。在扩展的AKNS系统中构造了Lax对，Riccati型自动Backlund变换（R-BT）和Wahlquist-Estabrook型自动Backlund变换（WE-BT）。通过R-BT获得一类孤子和两个类孤子解，并通过WE-BT获得非线性叠加公式。贝尔多项式方法给出了双线性形式和类N孤子解。基于所获得的解析解，讨论了由可变系数影响的波的传播特性。

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