Dynamical behaviors to the coupled Schrödinger-Boussinesq system with the beta derivative

In this paper, the modified auxiliary expansion method is used to construct some new soliton solutions of coupled Schrodinger-Boussinesq system that includes beta derivative. The new exact solution is obtained have a hyperbolic function, trigonometric function, exponential function, and rational function. These solutions might appreciate in laser and plasma sciences. It is shown that this method, provides a straightforward and powerful mathematical tool for solving the nonlinear problems. Moreover, the linear stability of this nonlinear system is analyzed. Keywords: Schrodinger-Boussinesq system; beta derivative; modulation instability analysis