Exact traveling wave solutions for some nonlinear evolution equations

Abstract

Abstract. In this paper, we obtain many traveling wave solutions for some nonlinear partial differential equations. The modified tanh-coth method with the symbolic computation is implemented for constructing multiple traveling wave solutions for the two dimensional coupled Burger's, ZK-MEW and one dimensional Ostrovsky equations. The results reveal that the implemented technique is very effective and convenient for solving nonlinear partial differential equations arising in mathematical physics.

Travelling wave solutions for (N + 1)-dimensional nonlinear evolution equations

“…Substituting (7) and (8) in eq. (6), we can rewrite the (N + 1)-dimensional generalized Boussinesq eq.…”

“…Equations (2), (3) and (4) Different numerical methods, such as Jacobi elliptic function method [4], variational iteration method [5][6][7], tanh function method [8][9][10][11], homotopy perturbation method [12][13][14][15], direct algebraic method [16], manifold theory [17], integral method [18] and so on, have been proposed by various authors for solving nonlinear evolution equation. More recently, He and Wu [19] proposed a straightforward and concise method called the exp-function method to explore exact solutions of the modified KdV equation.…”

Direct approach for solving nonlinear evolution and two-point boundary value problems

“…Accurate and fast numerical solution of nonlinear equations is of great importance due to their wide applications in scientific and engineering research. Different numerical methods have been proposed by various authors for solving nonlinear problems such as exp-function method [1][2][3][4][5][6], Jacobi elliptic function method [7], variational iteration method [8,9], tanh function method [10,11], (G /G)expansion method [12], homotopy perturbation method [13][14][15] and so on. However, practically there is no unified method that can be used to handle all types of nonlinearities.…”

Exact travelling wave solutions for some nonlinear (N+1)-dimensional evolution equations

“…Subsequently, Wazzan [22] used modified tanh-coth function method and obtained new solutions for some important nonlinear partial differential equations. More recently, Lee and Sakthivel [19] implemented modified tanhcoth function method for obtaining travelling wave solutions of two dimensional coupled Burger's equations.…”