Stability analysis of solutions for the sixth-order nonlinear Boussinesq water wave equations in two-dimensions and its applications

In the present study, we are concerned with the generalized Boussinesq equation including the singular sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional sixth-order nonlinear Boussinesq equation with constant coefficients. These solutions include symmetrical, non-symmetrical kink solutions, solitary pattern solutions, Jacobi and Weierstrass elliptic function solutions and triangular function solutions. The stability analysis for these solutions is discussed.