Analytical Cartesian solutions of the multi-component Camassa-Holm equations |
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| Authors: | Hongli An Liying Hou Manwai Yuen |
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| Affiliation: | 1. College of Science, Nanjing Agricultural University, Nanjing 210095, People’s Republic of China;2. College of Science, Nanjing Agricultural University, Nanjing 210095, People’s Republic of China lyhou@njau.edu.cn;3. Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, New Territories, Hong Kong nevetsyuen@hotmail.com |
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| Abstract: | Here, we give the existence of analytical Cartesian solutions of the multi-component Camassa-Holm (MCCH) equations. Such solutions can be explicitly expressed, in which the velocity function is given by u = b(t)+A(t)x and no extra constraint on the dimension N is required. The advantage of our method is that we turn the process of analytically solving MCCH equations into algebraically constructing the suitable matrix A(t). As the applications, we obtain some interesting results: 1) If u is a linear transformation on   | |
| Keywords: | Solution Analytical Cartesian solution Camassa-Holm equation Curve integration theory Multi- component Camassa-Holm equations |
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