New exact travelling wave solutions for the shallow long wave approximate equations

Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the shallow long wave approximate equations. New and more general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. The properties of the new formal solitary wave solutions are shown by some figures.