| 一类非线性偏微分方程组的直接解法 |
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| 引用本文： | 徐传友,曹锡芳.一类非线性偏微分方程组的直接解法[J].数学的实践与认识,2010,40(3). |
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| 作者姓名： | 徐传友 曹锡芳 |
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| 作者单位： | 1. 扬州大学数学科学学院,江苏,扬州,225002;阜阳师范学院数学与计算科学学院,安徽,阜阳,236041
2. 扬州大学数学科学学院,江苏,扬州,225002 |
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| 基金项目： | 阜阳师范学院青年基金项目(2008LQ10) |
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| 摘 要： | 根据Hopf-Cole变换法和试探函数法的基本思想,引入一个变换,并把它应用于求解(2+1)维破裂孤子方程组、(2+1)维Nizhnik-Novikov-Vesslov方程组和(2+1)维Broer-Kaup方程组,得到了这三个方程组的许多新的解析解,包括孤波解和奇异行波解.该方法也适用于其它方程组.
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| 关 键 词： | 破裂孤子方程组 Broer-Kaup方程组 直接解法 行波解 |
A Direct Method for Solving a Kind of Nonlinear Partial Differential Equation System |
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| XU Chuan-you,CAO Xi-fang.A Direct Method for Solving a Kind of Nonlinear Partial Differential Equation System[J].Mathematics in Practice and Theory,2010,40(3). |
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| Authors: | XU Chuan-you CAO Xi-fang |
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| Institution: | XU Chuan-you~(1,2),CAO Xi-fang~1 (1.Department of Mathematics Yangzhou University,Yangzhou 225002,China) (2.Department of Mathematics Fuyang Teachers College,Fuyang 236041,China) |
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| Abstract: | Introducing a new transformation according to the basic thoughts of HopfCole transformation and the trial function method,and applies it to the solution of(2+1)- dimensional breaking soliton system,(2+1)-dimensional Nizhnik-Novikov-Vesslov system and(2+1)-dimensional Broer-Kaup system,obtained many new analytic solutions to these three systems,including solitary wave solution and strange traveling wave solution.and the method is also suit to the other systems. |
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| Keywords: | breaking soliton system Broer-Kaup system direct approach travelling wave solution |
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