Abundant traveling wave solutions of the compound KdV-Burgers equation via the improved (G′/G)-expansion method

Abstract

In this article, we investigate the compound KdV-Burgers equation involving parameters by applying the improved G /G -expansion method for constructing some new exact traveling wave solutions including solitons and periodic solutions. The second order linear ordinary differential equation with constant coefficients is used, in this method. The obtained solutions are presented through the hyperbolic, the trigonometric and the rational functions. Further, it is significant to point out that some of our solutions are in good agreement for special cases with the existing results which validates our other solutions. Moreover, some of the obtained solutions are described in the figures.

New exact solutions to a KdV equation with drifting using multiple G′/G-expansion schemes

“…, (22) where G = G(ξ) satisfies (14). Substituting (22) along with (14) into (15) and then setting all the coefficients of (G /G) k for k = 0, 1, .…”

“…. , n) and then substituting these constants and the known general solutions of (14), which can be obtained by setting λ = 0 in (8)-(10), into (13), we obtain the explicit solutions of nonlinear differential (3).…”

“…This method can also be applied to fractional ODEs 11 . To extend the range of its applicability, the generalized G /G-expansion method 12 , the extended G /G-expansion method 13 and the improved G /Gexpansion method 14 have been developed. The nonlinear shallow water surface waves satisfy the Korteweg-de Vries (KdV) equation…”

Some new solutions of the (1+1)-dimensional PDE via the improved (G′/G)-expansion method

“…Naher and Abdullah [19] investigated the combined KdVMKdV equation to establish analytical solutions via this method while they [20] studied the (2+1)-dimensional modified Zakharov-Kuznetsov equation for obtaining traveling wave solutions by applying the same method. Naher et al [21] solved the compound KdV-Burgers equation via this method and so on.…”

On The Exact Solutions to Conformable Time Fractional Equations in EW Family Using Sine-Gordon Equation Approach

“…Exp function method [7,8] assumes the predicted solutions as a finite series of some particular functions. (G /G) expansion method [9,10] is an alternative that approaches the solution with a finite power series of a function satisfying a particular ODE. Trigonometric and hyperbolic type solutions to nonlinear PDEs can be determined by implementation of sine-cosine approach [11][12][13].…”