| Solving Kadomtsev—Petviashvili Equation via a New Decomposition and Darboux Transformation |
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| 引用本文： | FANEn－Gui. Solving Kadomtsev—Petviashvili Equation via a New Decomposition and Darboux Transformation[J]. 理论物理通讯, 2002, 37(2): 145-148 |
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| 作者姓名： | FANEn－Gui |
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| 作者单位： | InstituteofMathematics,FudanUniversity,Shanghai200433,China |
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| 基金项目： | Chinese Key Research Plan "Mathematical Mechanization and a Platform for Automated Reasoning"，上海市科委资助项目，中国博士后科学基金 |
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| 摘 要： | Recently,a new decomposition of the (2 1)-dimensional Kadomtsev-Petviashvili(KP) equation to a (1 1)-dimensional Broer-Kaup (BK) equation and a (1 1)-dimensional high-order BK equation was presented by Lou and Hu.In our paper,a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems.As application,new explicit soliton-like solutions with five arbitrary parameters for the BK equation,high-order BK equation and KP equation are obtained.
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| 关 键 词： | 非线性方程 KP方程 分解变换 Darboux变换 |
| 收稿时间： | 2001-06-25 |
Solving Kadomtsev-Petviashvili Equation via a New Decomposition and Darboux Transformation |
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| FAN En-gui. Solving Kadomtsev-Petviashvili Equation via a New Decomposition and Darboux Transformation[J]. Communications in Theoretical Physics, 2002, 37(2): 145-148 |
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| Authors: | FAN En-gui |
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| Affiliation: | Institute of Mathematics, Fudan University, Shanghai 200433, China |
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| Abstract: | Recently, a new decomposition of the (2+1)-dimensional Kadomtsev Petviashvili (KP) equation to a (1+1 )-dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order BK equation was presented by Lou andHu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derivedwith the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutionswith five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained. |
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| Keywords: | KP equation BK equation Darboux transformation exact solution |
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