Abstract
In this article, the exp-Φξ method is connected to search for new hyperbolic, periodic, and rational solutions of (1+1)-dimensional fifth-order nonlinear integrable equation and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. The obtained solutions consist of trigonometric, hyperbolic, rational functions and W-shaped soliton. Furthermore, 3D and 2D graphs are plotted by choosing the suitable values of the parameters involved.
Highlights
Consider the (1+1)-dimensional fifth-order nonlinear integrable equation
A new kind of W-shaped soliton solution is demonstrated and the other obtained solutions consist of trigonometric, hyperbolic, rational functions which are new
The graphical representation of the other solutions (u2, u3, u4, u5) for the (1 + 1)-dimensional fifth-order nonlinear integrable equation and (u7, u8, u9, u10) for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation is shown by Figures 2–5 and 7–10, respectively
Summary
Consider the (1+1)-dimensional fifth-order nonlinear integrable equation. In [1], Wazwaz proposed a new (1 + 1)dimensional fifth-order nonlinear integrable equation of the form uttt − utxxxx − 4 (uxut)xx − 4 (uxuxt)x = 0,. Many effective methods have been proposed to solve the NLEEs, such as the Hirota method [1], Hereman-Nuseir method [2], inverse scattering transformation [4], Painlevetechnique [5], Backlund transformation [6], Darboux transformation [7, 8], Binary-Bell-polynomial scheme [9], first integral method [10, 11], (G/G)−expansion method [12], the exp(−Φ(ξ)) expansion method [13], Exp-function method [14], ansatz method [15], sine-Gordon expansion method [16, 17], the trial equation method [18, 19], homotopy asymptotic [20], and so on.
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