Wronskian solutions of the Boussinesq equation—solitons, negatons, positons and complexitons

Abstract

A Wronskian formulation is presented for the Boussinesq equation, which involves a broad set of sufficient conditions consisting of linear partial differential equations. The representative systems of the differential equations in the sufficient conditions are explicitly solved. The obtained solution formulae provide us with a comprehensive approach to construct exact and explicit solutions to the Boussinesq equation, by which solitons, negatons, positons and complexitons are computed for the Boussinesq equation.