Abstract
In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. In this paper, the simple equation method (SEM) is used to obtain new traveling wave solutions of gKdv and Ske. The physical properties of the obtained solutions are graphically illustrated using suitable parameters. The computational simplicity of the proposed method shows the robustness and efficiency of SEM.
Highlights
The application of nonlinear partial differential equations is not limited to areas of mathematics exclusively and applicable in other science aspects like physics and engineering
For the solutions of the Sawada Kotera equation, solutions obtained in Equation (44), Equation (45) and Equation (46) are nearly similar to the solutions obtained by Ref
The rest of the solutions obtained in this paper are unique solutions which have not been stated before in existing literature. These solutions are applicable in long waves of small or moderate amplitude in shallow water of uniform depth, nonlinear acoustic waves in an inharmonic lattice, Alfven waves in a collisionless plasma, and a lot more important physical phenomena
Summary
The application of nonlinear partial differential equations is not limited to areas of mathematics exclusively and applicable in other science aspects like physics and engineering. In the study of waves dynamics, Korteweg-deVries equation (gKdv) and Sawada-Kotera equation (Ske) are applied in nonlinear evolution equation of long waves of small or moderate amplitude in shallow water of uniform depth, nonlinear acoustic waves in an inharmonic lattice, Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. Methods of obtaining analytical or exact solution to the gKdv and Ske nonlinear partial differential equations used by other researchers include the sine-cosine method [1], an auto-Blackland transformation [2], Hirota direct method [3], the projective Riccati equation method [4], the He’s varia-. The simple equation method for solving nonlinear partial differential equations has gained a lot of attention from researchers due to its simplicity and ability to extract novel traveling wave solutions.
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