New Solitary Wave and Multiple Soliton Solutions for the Time-space Fractional Boussinesq Equation

The aim of this paper are in two fold: First, introduce a new simplified bilinear method based on a transformation method combined with the Hirota bilinear sense. Second, apply this new technique to study the time-space fractional Boussinesq equation. To the best of my knowledge, the proposed work present new N-soliton solutions of the fractional Boussinesq equation. These new exact solutions extend previous results and help us to explain the properties of multidimensional nonlinear solitary waves in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.