Fully resonant soliton interactions in the Whitham–Broer–Kaup system based on the double Wronskian solutions

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

“…We point out that Solutions (2.21a) and (2.21b) can display a variety of multi-soliton structures with unequal numbers of asymptotic solitons as t → ±∞, and they are more general than the results obtained in Ref. [32] in the sense that the former coincides with the latter when p 0 = 0.…”

“…(v) In Section 6, we address the conclusions of this work and compare the results with those obtained in Ref. [32].…”

“…(N is in general not equal to M) [32], which include Solutions (2.8) with p 0 = 0 as a very special case. That inspires us to guess that this system also admits the following general determinant solutions:…”

“…Recently, based on the asymptotic analysis method developed for the KPII soliton solutions [5], Ref. [32] has studied the soliton solutions in terms of two double Wronskians for the WBK system. The results show that the soliton solutions are linearly combined of two fully-resonant multi-soliton configurations.…”

“…Hence, we derive a new family of double Wronskian solutions which are more general than those obtained in Refs. [20,32] because an additional free parameter is included. (ii) In Section 3, we expand the new double Wronskians by the Laplace expansion technique and Binet-Cauchy theorem, and further analyze their algebraic properties so as to find the parametric condition for the non-singular, non-trivial and irreducible soliton solutions.…”