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| Investigation of Multi-soliton, Multi-cuspon Solutions to the Camassa-Holm Equation and Their Interaction |
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Citation： |
Xiaozhou LI,Yan XU,Yishen LI.Investigation of Multi-soliton, Multi-cuspon Solutions to the Camassa-Holm Equation and Their Interaction[J].Chinese Annals of Mathematics B,2012,33(2):225~246 |
| Page view： 1830
Net amount： 1644 |
Authors： |
Xiaozhou LI; Yan XU; Yishen LI; |
Foundation： |
the National Natural Science Foundation of China (Nos.10971211, 11031007), the Foundation for the Author of National Excellent Doctoral Dissertation of China (No.200916), the Foundation for the Author of National Excellent Doctoral Dissertation of the Chinese Academy of Sciences, Program for New Century Excellent Talents in University of China (No.09-0922) and the Fundamental Research Funds for the Central Universities (No.WK0010000005). |
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| Abstract： |
The authors study the multi-soliton, multi-cuspon solutions to the Camassa-Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of parameters for multi-soliton and multi-cuspon solutions, especially for $n\geq3$ case. The numerical method (the so-called local discontinuous Galerkin (LDG) method) is also used to simulate the solutions and give the comparison of exact solutions and numerical solutions. The numerical results for the two-soliton and one-cuspon, one-soliton and two-cuspon, three-soliton,three-cuspon, three-soliton and one-cuspon, two-soliton and two-cuspon, one-soliton and three-cuspon, four-soliton and four-cuspon are investigated by the numerical method for the first time, respectively. |
Keywords： |
Camassa-Holm equation,Local discontinuous Galerkin method,Multi-soliton, Multi-cuspon |
Classification： |
65M60,35Q53 |
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