Nonlinear Dynamics

, Volume 73, Issue 1–2, pp 485–498 | Cite as

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

  • Tao Xu
  • Yi Zhang
Original Paper


With the aim of exploring whether the (1+1)-dimensional coupled nonlinear evolution equations admit abundant soliton interactions, like the cases in the Kadomtsev–Petviashvili II equation, we in this paper study the double Wronskian solutions to the Whitham–Broer–Kaup (WBK) system. We give the parametric condition for two double Wronskians to generate the non-singular, non-trivial and irreducible soliton solutions. Via the asymptotic analysis of two double Wronskians, we show that the soliton solutions of the WBK system is in general linearly combined of fully resonant (M,N)- and (M−1,N+1)-soliton configurations. It turns out that the WBK system can exhibit various complex soliton structures which are different pairwise combinations of elastic, confluent and divergent interactions. From a combinatorial viewpoint, we also explain that the asymptotic solitons of a [(M,N),(M−1,N+1)]-soliton solution are identified by a pair of Grassmannian permutations.


Soliton interactions Whitham–Broer–Kaup system Asymptotic analysis Double Wronskian 



TX would like to thank the beneficial direction of Professor Gino Biondini when staying in the State University of New York at Buffalo as a visiting scholar from 2008 to 2009. This work has been supported by the Science Foundation of China University of Petroleum, Beijing (Grant No. BJ-2011-04), by the Special Funds of the National Natural Science Foundation of China (Grant No. 11247267), and by the National Natural Science Foundation of China (Grant No. 11071257).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of ScienceChina University of PetroleumBeijingChina

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