| 一类非线性波方程的尖峰孤立子解 |
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| 引用本文： | 刘煜,吕卫东.一类非线性波方程的尖峰孤立子解[J].山西大学学报(自然科学版),2010,33(1). |
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| 作者姓名： | 刘煜 吕卫东 |
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| 作者单位： | 1. 河南电力试验研究院,河南郑州,450052
2. 河南科技大学,河南洛阳,471003 |
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| 基金项目： | 河南电力试验研究院科研基金 |
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| 摘 要： | 根据尖峰孤立子解的特点,提出了待定系数法求非线性方程尖峰孤子解的方法,并利用该方法求出了一类非线性波方程u_t+2ku_x-u_(xxt)+(b+1)uu_x=bu_xu_(xx)+uu_(xxx)-γ·u_(xxx)的几类尖峰孤立子解.几个重要的非线性方程,如CH(Camassa-Holm)方程、DP(Degasperis-Procesi)方程和带色散项的DP方程等,作为该方程的特殊情形也得到了若干新的尖峰孤立子解.文献中已有的结果成为本文结果的特例.本文方法也适用于求其他多个非线性方程的尖峰孤立子解.
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| 关 键 词： | 非线性波方程 尖峰孤立子解 待定系数法 |
Peaked Soliton Solutions for a Kind of Nonlinear Wave Equation |
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| LIU Yu,L Wei-dong.Peaked Soliton Solutions for a Kind of Nonlinear Wave Equation[J].Journal of Shanxi University (Natural Science Edition),2010,33(1). |
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| Authors: | LIU Yu L Wei-dong |
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| Institution: | LIU Yu,L(U) Wei-dong |
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| Abstract: | Based on the characteristics of peaked soliton solutions,the undetermined coefficient method for solving nonlinear equations for their peaked soliton solutions is submitted and the several kinds of peaked soliton solutions are obtained for nonlinear wave equation,u_t+2ku_x-u_(xxt)(b+1)uu_x=bu_xu_(xx)+uu_(xxx)-γ·u_(xxx),by means of the method.Some new peaked soliton solutions are also obtained for CH(Camassa-Holm)equation,DP(Degasperis-Procesi)equation and DP equation with the dispersion term.The solutions given in references are the special cases of the solutions.Moreover,the method can also be used for solving many other nonlinear equations. |
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| Keywords: | nonlinear wave equation peaked soliton solutions undetermined coefficient method |
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