New Traveling Wave Solutions of the Boussinesq Equation Using a New Generalized Mapping Method - Hu, Xuegang; Wu, Yong Hong; Ling, Li (World Academic Publishing, 2013)
In this paper, a generalized mapping method for finding the exact traveling wave solutions of a nonlinear partial differential equation is discussed. Firstly, some new solutions of an auxiliary ordinary differential equation are introduced. They are then used to generate new exact solutions for the Boussinesq equation. The new solutions are then grouped into ten families and the properties of each family of solutions are demonstrated. We should also emphasize here that the developed method can also be applied to a large variety of nonlinear partial differential equations in physics and mechanics.