| Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations |
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| 引用本文： | LIU Cheng-Shi. Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations[J]. 理论物理通讯, 2008, 49(2): 291-296 |
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| 作者姓名： | LIU Cheng-Shi |
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| 作者单位： | Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China |
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| 摘 要： | Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
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| 关 键 词： | 数学物理方法 非线性数学物理方程 孤波解 对称群 非线性偏微分方程 |
| 收稿时间： | 2006-12-30 |
Solution of ODE u'+p(u)(u')2+q(u)=0 andApplications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations |
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| LIU Cheng-Shi. Solution of ODE u'+p(u)(u')2+q(u)=0 andApplications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations[J]. Communications in Theoretical Physics, 2008, 49(2): 291-296 |
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| Authors: | LIU Cheng-Shi |
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| Affiliation: | Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China |
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| Abstract: | Under the travelling wave transformation, some nonlinear partialdifferential equations such as Camassa-Holm equation, High-order KdVequation,etc., are reduced to an integrable ODE expressed byu'+p(u)(u')2+q(u)=0 whose general solution can be given. Furthermore, combining completediscrimination system for polynomial, the classifications of allsingle travelling wave solutions to these equations are obtained.The equation u'+p(u)(u')2+q(u)=0 includes the equation (u')2=f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These completeresults cannot be obtained by any indirect method. |
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| Keywords: | classification of travelling wave solution symmetry group nonlinear partial differential equation |
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