New Soliton Solutions And Soliton Interactions In The Whitham-Broer-Kaup System

As an important branch of nonlinear science,the soliton has a wide range of applications in the fields of plasma physics,fluid mechanics,nonlinear optics and so on.It has been an important toptic to study the interaction properties of solitons in the integrable nonlinear systems.This dissertation is devoted to studying new soliton solutions and their interaction properties of the Whitham-Broer-Kaup system arising in shallow water.The main contents include the following four aspects: First,based on the Darboux transformation method and the Wronskian technique,we construct and veifty a family of generalized double Wronskian solutions.Second,we analyze the algebraic properties of the generalized double Wronskians to obtain the parametric conditions for nonsingular,nontrivial and nondegenerate soliton solutions.Third,by analyzing the asymptotic behavior of the generalized double Wronskians as t ? ??,we reveal the new soliton solutions are linearly combined of two fully-resonant soliton structures,and determine the analytical expressions of asymptotic solitons and their associated index pairs.Finally,we present an algebraic algorithm to determine all the asymptotic solitons of the new soliton solutions and the asymptotically dominant exponentials in different regions of the xt-plane.By drawing figures on Mathematica,we discuss the soliton resonant interaction properties with some specific parameters.In this dissertation,we develop some new Wronskian identities,and apply the Wronskian-based asymptotic analysis method to a(1+1)-dimensional nonlinear system.The obtained soliton interaction properties may help to explain some solitary-wave phenomena in fluid dynamics.