Solitary waves, periodic waves, and a stability analysis for Zufiria's higher-order Boussinesq model for shallow water waves

Abstract

Zufiria's higher-order Boussinesq model for water waves is reappraised. Heretofore solutions of this equation have been obtained numerically. Firstly, we show that in fact this model has exact solutions. An algebraic method is applied to construct solitary wave solutions, doubly-periodic (cnoidal-type) wave solutions and a range of other solutions of physical interest. Secondly, we show that this model has a nice property which leads to a global energy type argument for linear stability of the solitary waves.