广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解

J4 ›› 2014, Vol. 31 ›› Issue (6): 663-669.

广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解

孟祥花许瑞麟许晓革

北京信息科技大学理学院北京 100192

收稿日期:2014-05-12 修回日期:2014-08-08 出版日期:2014-11-28 发布日期:2014-11-17
通讯作者: 孟祥花(1981-), 山东邹平人，博士，讲师，研究方向为孤子理论及其应用. E-mail:xhmeng@bistu.edu.cn
基金资助:
Supported by the National Natural Science Foundation of China under Grant No. 61072145 and the Scientific Research Project of Beijing Educational Committee (No. SQKM201211232016) and Beijing Excellent Talent Training Project (2013D005007000003)

Auto-Backlund transformation and novel exact analytic solutions for the generalized variable-coefficient Burgers-Kadomtsev-Petviashvili equation

MENG Xiang-hua, XU Rui-lin, XU Xiao-ge

School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received:2014-05-12 Revised:2014-08-08 Published:2014-11-28 Online:2014-11-17

摘要/Abstract

摘要： 应用Painlevé分析法研究了广义变系数Burgers-Kadomtsev-Petviashvili方程。结果显示该方程不具有Painlevé性质。通过截断的Painlevé展开方法，在条件 ( 为任意常数)下, 得到了该方程的自B?cklund变换。基于自B?cklund变换，给出了一些新的解析解如多孤子解和周期解。

关键词: 广义变系数Burgers-Kadomtsev-Petviashvili方程, Painlevé分析, 自B?cklund变换, 解析解

Abstract: The generalized variable-coefficient Burgers-Kadomtsev-Petviashvili equation is investigated employing the Painlevé analysis technique. It has shown that the equation does not possess the Painlevé property. Via the truncated Painlevé expansion method and under the condition ( is a constant), we have derived an auto-B?cklund transformation for the generalized variable- coefficient Burgers-Kadomtsev-Petviashvili equation. Based on the obtained auto-B?cklund transformation, some novel exact analytic solutions are given, including multiple soliton and periodic solutions.

Key words: variable-coefficient Burgers-Kadomtsev-Petviashvili equation, Painlevé analysis, auto- B?cklund transformation, analytic solutions

中图分类号:

O175.29

孟祥花许瑞麟许晓革. 广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解[J]. J4, 2014, 31(6): 663-669.

MENG Xiang-hua, XU Rui-lin, XU Xiao-ge. Auto-Backlund transformation and novel exact analytic solutions for the generalized variable-coefficient Burgers-Kadomtsev-Petviashvili equation[J]. J4, 2014, 31(6): 663-669.

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