Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability

The weakly nonlinear Hamiltonian theory for two-dimensional irrotational shallow water waves is formulated. Zufiria’s higher-order Boussinesq model for waves on water of finite depth is obtained. The formulation Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. By implementing different types of extended direct algebraic method, we show that in fact this model has new exact solutions. An extended direct algebraic methods are applied to construct solitary wave solutions.