| 利用符号计算求解高阶非线性演化方程的新方法 |
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| 引用本文： | 史振华,夏铁成.利用符号计算求解高阶非线性演化方程的新方法[J].上海大学学报(自然科学版),2011,17(3):270-274. |
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| 作者姓名： | 史振华 夏铁成 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 基金项目： | 国家自然科学基金资助项目(61072147,11071159); 上海市自然科学基金资助项目(09ZR1410800); 国家数学机械化重点实验室合作交流基金资助项目(KLMM0806); 上海市教委基金资助项目(J50101); 上海市重点学科建设资助项目(S30104) |
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| 摘 要： | 用〔G′/G〕扩展法进一步求解(2+1)维Bogoyavlenskii破裂孤子方程和(3+1)维Kadom tsev-Petviashvili(K-P)方程,成功得到双曲函数解、三角函数解和有理解.结果表明,该方法对于求解高维非线性偏微分方程同样有效.
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| 关 键 词： | G′/G〕扩展法 符号计算 Bogoyavlenskii破裂孤子方程 Kadomtsev-Petviashvili(K-P)方程 |
New Method to Solve High-Dimensional Nonlinear Evolution Equations with Symbolic Computation |
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| SHI Zhen-hua,XIA Tie-cheng.New Method to Solve High-Dimensional Nonlinear Evolution Equations with Symbolic Computation[J].Journal of Shanghai University(Natural Science),2011,17(3):270-274. |
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| Authors: | SHI Zhen-hua XIA Tie-cheng |
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| Institution: | SHI Zhen-hua,XIA Tie-cheng(College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | In this paper,we seek exact solutions to the(2+1)-dimensional Bogoyavlenskii’s breaking soliton equation and(3+1)-dimensional Kadomtsev-Petviashvili(K-P) equation by 〔G′/G〕-expansion method,and obtain non-traveling wave solutions including hyperbolic function solutions,trigonometric function solutions and rational solutions.The method is effective for high-dimensional NLPDEs in mathematical physics. |
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| Keywords: | G′/G〕-expansion method symbolic computation Bogoyavlenskii’s breaking soliton equation Kadomtsev-Petviashvili(K-P) equation |
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