Exact solutions of the Kudryashov-Sinelshchikov equation by modified exp-function method

Abstract

In this paper, the modified exp-function method is used to seek generalized wave solutions of Kudryashov-Sinelshchikov equation. As a result, some new types of exact traveling wave solutions for arbitrary α, β are obtained which include exponential function, hyperbolic function and trigonometric function. The related results are extend. Obtained results clearly indicate the reliability and efficiency of the modified expfunction method.

Traveling Wave Solutions of Nonlinear Evolution Equations Via the Modified Simple Equation Method

“…These solutions are general closed form traveling wave solutions which are soliton, and periodic wave solution respectively. From the above solution, the solutions (20) and (24) are represents in the exponential form where the solutions (21) to (23) and (25) to (27) are represents in terms of trigonometric functions. The solutions (22) and (26) are represents periodic wave solution and the solutions (23) and (27) are represents singular soliton solutions.…”

“…Consequently diverse groups of researchers have been working vigorously to develop effective methods for obtaining close form or exact solutions to NLEEs. That's why, recently several methods have been establish to explore exact solution, such as the nonlinear transform method [1], the functional variable method [2], the homogeneous balance method [3,4], the direct algebraic method [5], the rank analysis method [6], the Jacobi-elliptic function expansion method [7], the complex hyperbolic function method [8], the tanh-function method [9], the inverse scattering transform [10], the Exp-function method [11][12][13], the sine-cosine method [14], the first integration method [15], the auxiliary parameter method [16], the Painleve expansion method [17], the Adomian decomposition method [18], the generalized Riccati equation method [19], the Lie group symmetry method [20], the modified Exp-function method [21], the perturbation method [22], the exp(−Φ(η)) -expansion method [23][24][25], the ( / )-expansion method [26][27][28], the asymptotic method [29], the improve ( / )-expansion method [30], the modified simple equation method [31][32][33][34] etc. The recently developed modified simple equation method is getting popularity in use because of its straight forward calculation procedure but the method did not applied to solve if the balance number is greater than 2.…”

Traveling wave solutions of some nonlinear evolution equations

“…In recent years, there become significant improvements in finding the exact solutions of NLEEs. Many effective and powerful methods have been established and improved [25,27], such as, the Hirota's bilinear transformation method [13,14], the tanh-function method [16,20,26], the (G 0 /G)-expansion method [3][4][5][6]21], the Exp-function method [12,7,19,18], the homogeneous balance method [24,31], the F-expansion method [32], the Adomian decomposition method [2], the homotopy perturbation method [17], the extended tanh-method [1,10], the auxiliary equation method [22], the Jacobi elliptic function method [8], Weierstrass elliptic function method [15], modified Exp-function method [11], and the modified simple equation method [28][29][30].…”

Traveling wave solutions of the (2+1)-dimensional Zoomeron equation and the Burgers equations via the MSE method and the Exp-function method

“…In recent years, there become significant improvements in finding the exact solutions of NLEEs. Many effective and powerful methods have been established and improved, such as, the Hirota's bilinear transformation method [1,2], the tanh-function method [3,4], the (G 0 /G)-expansion method [5][6][7][8][9][10][11][12][13], the Exp-function method [14][15][16][17][18], the homogeneous balance method [19,20], the F-expansion method [21], the Adomian decomposition method [22], the homotopy perturbation method [23], the extended tanh-function method [24,25], the auxiliary equation method [26], the Jacobi elliptic function method [27], the Weierstrass elliptic function method [28], the modified Exp-function method [29], the modified simple equation method [30][31][32][33], and so on.…”