An improved generalized F-expansion method and its application to the (2+1)-dimensional KdV equations

New periodic wave solutions for nonlinear evolution equations with variable coefficients via mapping method

“…As a result, many exact travelling wave solutions are obtained which include new soliton-like solutions, trigonometric function solutions and rational solutions. When the modulus m −→ 1 and m −→ 0 some of the obtained solutions degenerate as solitary wave solutions which cannot be obtained by the F-expansion methods [13][14][15][16][17]. It seems that the generalized F-expansion method is more effective and simple than other methods and a lot of solutions can be obtained in the same time.…”

Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation

“…Li and Wang [9] used the sub-ODE method to find the exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms, which provided an important theoretical basis for developing numerical methods of the generalized KdV-mKdV equation. Recently, analytic solutions of the (2+1)-dimensional KdV equation and the interactions between the solutions have been investigated frequently [10][11][12][13]. But numerical methods relevant to the generalized (2+1)-dimensional KdV-mKdV equation have not yet been reported in the current literatures.…”

Evaluation of two-dimensional ZK-MEW equation using the Exp-function method

“…Taking advantage of the generalized solitonary solutions, we can recover some known solutions obtained by the most existing methods such as decomposition method [11,12], tanhfunction method [13][14][15], algebraic method [16], extended Jacobi elliptic function expansion method [17,18], F-expansion method [19,20], auxiliary equation method [21] and others. By the help of symbolic mathematical tools, the solution procedure of this method is of utter simplicity and the method can be easily extended to all kinds of NLEEs.…”