New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions |
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Authors: | Tao Xu Changjing Liu Fenghua Qi Chunxia Li Dexin Meng |
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Affiliation: | 1. College of Science, China University of Petroleum, Beijing 102249, China;2. School of Information, Beijing Wuzi University, Beijing 101149, China;3. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China |
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Abstract: | In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new double Wronskian functions as t → ±∞, we make a complete characterization of asymptotic solitons for the non-singular, non-trivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fully-resonant multi-soliton configurations, in each of which the amplitudes, velocities and numbers of asymptotic solitons are in general not equal as t → ±∞. To illustrate, we present the figures for several examples of soliton interactions occurring in the WBK system. |
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Keywords: | Soliton interactions Whitham-Broer-Kaup system asymptotic analysis double Wronskian 35Q51 37K40 |
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