| 非线性波动方程最简形式尖峰孤子解的存在性及求解方法 |
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| 引用本文： | 刘煜,刘伟庆. 非线性波动方程最简形式尖峰孤子解的存在性及求解方法[J]. 安徽大学学报(自然科学版), 2013, 0(3) |
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| 作者姓名： | 刘煜 刘伟庆 |
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| 作者单位： | 河南省电力公司电力科学研究院;河南科技大学数学与统计学院; |
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| 基金项目： | 河南省电力公司电力科学研究院科研基金资助项目 |
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| 摘 要： | 以经典的Camassa-Holm方程为例,讨论非线性波动方程存在最简形式尖峰孤子解的必要和充分条件,归纳出求取该型解的一般性方法,并通过求解Oliver水波方程、广义KdV方程K(2,2,1)和(2+1)维Nizhnik-Novikov-Veselov方程对该方法做验证,验证表明该方法是简便、有效的.运用该方法分析判断和求解了多个非线性波动方程,结果表明存在该型解的非线性波动方程为数不少.该方法也可用于2类紧孤子解存在性的分析和求解.
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| 关 键 词： | 非线性波动方程 最简形式尖峰孤子解 Oliver水波方程 广义KdV方程K(2,2,1) (2+1)维Nizhnik-Novikov-Veselov方程 |
The existence and solving method for the simplest form peakon solution to nonlinear wave equations |
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| Abstract: | By taking the classical Camassa-Holm equation as an example,the necessary and sufficient conditions for the existence of the simplest form of peakon solution(SFPS) to nonlinear wave equations were discussed.A solution to obtaining the SFPS was proposed and was verified to be simple and effective by solving three nonlinear wave equations,i.e.,Oliver water wave equation,generalized KdV equation K(2,2,1) and(2+1)-dimensional Nizhnik-Novikov-Veselov equation.The results of judging and solving many nonlinear equations by using this method indicated that many nonlinear equations had the SFPS.This method could also be used for obtaining two kinds of compacton solutions. |
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| Keywords: | nonlinear wave equation the simplest form peakon solution Oliver water wave equation generalized KdV equation K(2,2,1) (2+1)-dimensional Nizhnik-Novikov-Veselov equation |
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