| 非线性偏微分方程的约化和精确解 |
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| 引用本文： | 叶彩儿,潘祖梁. 非线性偏微分方程的约化和精确解[J]. 高校应用数学学报(英文版), 2003, 18(2): 179-185. DOI: 10.1007/s11766-003-0022-5 |
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| 作者姓名： | 叶彩儿 潘祖梁 |
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| 作者单位： | Ye Caier Pan ZuliangDept. of Math.,Zhejiang Univ.,Hangzhou 310027,China. |
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| 基金项目： | Supported by the Natural Science Foundation of Zhejiang Province(1 0 2 0 3 7) |
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| 摘 要： | § 1 IntroductionSeeking the exact solutions of the nonlinear partial differential equation is one of thevery importantsubjectin PDE research.Up to now,many methods offinding the exact so-lutions for NLPDE are constructed,such as inverse scattering transformation(IST) [1 ] ,Liepoint symmetry and similar reductions[2 ,3] ,B cklund[4— 6] and Cole-Hofe transformations,Hirota s bilinear method[7] ,the homogeneous balance method[8,9] ,tanh function method[1 0 ]and so on.In this paper,we giv…
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| 收稿时间： | 2002-05-17 |
Reduction of nonlinear partial differential equation and exact solutions |
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| Caier Ye,Zuliang Pan. Reduction of nonlinear partial differential equation and exact solutions[J]. Applied Mathematics A Journal of Chinese Universities, 2003, 18(2): 179-185. DOI: 10.1007/s11766-003-0022-5 |
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| Authors: | Caier Ye Zuliang Pan |
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| Affiliation: | Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China;Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China |
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| Abstract: | Nonlinear partial differetial equation(NLPDE) is converted into ordinary differential equation(ODE) via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained. |
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| Keywords: | nonlinear partial differential equation ordinary differential equation exact solutions solitary solutions. |
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