New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Xu, Tao; Liu, Changjing; Qi, Fenghua; Li, Chunxia; Meng, Dexin
• Is Part Of: Journal of nonlinear mathematical physics. Volume 24:Issue 1(2017)
• Page Start: 116
• Page End: 141
• Publication Date: 2017-01-02
• Subjects: Soliton interactions -- Whitham-Broer-Kaup system -- asymptotic analysis -- double Wronskian -- 35Q51 -- 37K40; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2017.1282248
• Languages: English
• ISSNs: 1402-9251

Abstract

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.