| mKdV和mBBM方程的新型孤子解 |
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| 引用本文： | 刘煜,刘伟庆,吕卫东.mKdV和mBBM方程的新型孤子解[J].安徽大学学报(自然科学版),2012(4):37-42. |
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| 作者姓名： | 刘煜 刘伟庆 吕卫东 |
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| 作者单位： | 河南电力试验研究院情报所;河南科技大学数学与统计学院 |
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| 基金项目： | 河南电力试验研究院科研基金资助项目 |
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| 摘 要： | 尖峰孤子解和紧孤子解是非线性方程的新型孤子解.利用相关文献提出的方法分别研究修正的KdV方程(mKdV)和修正的BBM方程(mBBM),得到3种形式的孤子解:尖峰孤子解、双峰孤子解和尖峰紧孤子解.通过数值模拟得到解的图像,其中之一为双峰形的孤立波.这些结果进一步丰富了这2个非线性波方程的精确解的形式和内容.该文提出的3个拟解之一还可以用于其他多个非线性波方程,如:Klein-Gordon方程、Ф4方程、Sine-Gordon方程和Landau-Ginzburg-Higgs方程.
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| 关 键 词： | mKdV方程 mBBM方程 尖峰孤子解 双峰孤子解 尖峰紧孤子解 |
New type soliton solutions to mKdV and mBBM equations |
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| LIU Yu,LIU Wei-qing,LV Wei-dong.New type soliton solutions to mKdV and mBBM equations[J].Journal of Anhui University(Natural Sciences),2012(4):37-42. |
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| Authors: | LIU Yu LIU Wei-qing LV Wei-dong |
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| Institution: | 1.Department of Information,Henan Electric Power Research Institute,Zhengzhou 450052,China; 2.School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471003,China) |
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| Abstract: | Peakon solution and compacton solution are new type soliton solutions to nonlinear wave equations.In this paper,we researched two nonlinear wave equations-modified Korteweg-de Vries(mKdV) equation and modified Benjamin-Bona-Mahony(mBBM)equation,respectively,and obtained three kinds of new type soliton solutions: peakon solutions,double-peak soliton solutions and peaked compacton solution.These results further enriched the patterns of explicit and exact solutions to mKdV and mBBM equations.The graphs of these solutions were given through numerical simulation,one of which was a double-peak solitary wave.One of three ansatz solutions proposed could also be used in many other nonlinear wave equations such as Klein-Gordon equation,4equation,Sine-Gordon equation and Landau-Ginzburg-Higgs equation. |
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| Keywords: | mKdV equation mBBM equation peakon solution double-peak soliton solution peaked compacton solution |
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