In this paper, we extend the (,1) G G G ′-expansion method to the (2+1)-dimensional Kadomstev-Petivshvili (KP) equation. As a result, hyperbolic function solution, trigonometric function solution and rational solution are obtained.

Ji-Huan He systematically studied the inverse problem of calculus of variations. This note reveals that the semi-inverse method also works for a generalized KdV-mKdV equation with nonlinear terms of any orders.

In this paper, the extended simplest equation method is implemented to find the exact solutions for the Boussinesq equation. The efficiency of this method for constructing these exact solutions has been demonstrated. It is shown that the proposed method is direct, concise and effective, and can be used for many other nonlinear evolution equations.

Applying the first integral method, and combining the computation software, Maple, we find exact traveling wave solutions of the mKdV equation. The method is based on the ring theory of commutative algebra.

Abstract. The extended simplest equation method is used to construct exact solutions of the modified Benjamin-Bona-Mahony (mBBM) equation. The results obtained are in the form of hyperbolic, trigonometric, and rational functions. Throughout the paper, all the calculations are made with the aid of the Maple packet program. The method is more effective and simple than other method and can be used for many other nonlinear evolution equations.