New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions
| Autor: | Chun-Xia Li, Tao Xu, Fenghua Qi, Dexin Meng, Changjing Liu |
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| Rok vydání: | 2021 |
| Předmět: |
Determinant identities
Asymptotic analysis Wronskian 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Variation of parameters 01 natural sciences Superposition principle Nonlinear Sciences::Exactly Solvable and Integrable Systems Amplitude Transformation (function) 0103 physical sciences 010307 mathematical physics Soliton 0101 mathematics Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Mathematics |
| Zdroj: | Journal of Nonlinear Mathematical Physics. 24:116 |
| ISSN: | 1776-0852 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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