THE TRAVELING WAVE SOLUTIONS AND APPROXIMATE SOLUTIONS FOR BOUSSINESQ EQUATIONS

First, all possible traveling wave solutions of the Boussinesq equations in shallow water theory are discussed. It is shown that these solutions are periodic waves, convex solitary waves and concave solitary waves. Second, by using a reductive perturbation method, shallow water equation with a small damping term have been reduced to a single KdV-Burgers equation, from which the approximate solution of the original equations can be expressed.