New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

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, nontrivial and irreducible soliton solutions. It turns out that the solutions are the linear superposition of two fullyresonant 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.

Multiple lump solutions of the (2+1)-dimensional sawada-kotera-like equation

“…Nonlinear evolution equations can be used to simulate various nonlinear phenomena in the real world, which appear in fluid mechanics [1][2][3], optical fibers [4], applied mathematics [5][6][7], chemistry and biology [8][9][10], etc. In recent years, searching for exact solutions of nonlinear evolution equations has attracted considerable attention, such as lump solutions [11][12][13][14][15][16], soliton solutions [17][18][19][20][21] and breather solutions [22][23][24][25].…”