Soliton Solutions of Wronskian Form to theNonlocal Boussinesq Equation

Abstract

We investigate how one may write the soliton solutions of a nonlocal Boussinesq equation in Wronskian form, and subsequently prove the existence of N-soliton solutions making use of the bilinear form of this equation. This technique also allows us to construct a bilinear Bäcklund transformation for this equation, mapping N-soliton solutions on (N+1)-soliton solutions. Our analysis extends the results previously obtained by Hirota for the Classical Boussinesq system to actual (c≠ 0) “pq=c”-reductions performed on Wronskians.