Application of tan(ϕ/2)-expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity

In this paper, the improved tan(Φ(ξ)/2)-expansion method is proposed to seek more general exact solutions of the new partial differential equation. Being concise and straightforward, this method is applied to the Biswas–Milovic equation (BME). The exact particular solutions containing four types hyperbolic function solution, trigonometric function solution, exponential solution and rational solution. We obtained the further solutions comparing with other methods as [13]. Recently this method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering and physics fields. It is shown that this method, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving problems in nonlinear optic.