Abstract
Abstract In this work, we study the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We employ the extended tanh function method and the simple equation method to achieve analytical soliton solutions. Moreover, numerical treatment for this equation is introduced by the finite difference method. We justify the accuracy of the obtained results by exhibiting illustrative tables and proper graphs.
Highlights
The Kadomtsev-Petviashvili (KP) equation is one of the basic soliton equations and it has fundamental signi cance in mathematical physics
In this work, we study the ( + )-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation
We employ the extended tanh function method and the simple equation method to achieve analytical soliton solutions. Numerical treatment for this equation is introduced by the nite di erence method
Summary
The Kadomtsev-Petviashvili (KP) equation is one of the basic soliton equations and it has fundamental signi cance in mathematical physics. The extended tanh function method [17,18,19] and the simple equation method [20, 21], will be used to nd analytical solutions to the above-mentioned DJKM equation. The nite di erence method will be employed to obtain numerical solution to the DJKM equation. The DJKM equation describes the long water waves with frequency dispersion and weakly nonlinear restoring forces. This equation has been investigated by employing a variety of poweful methods such as, the Hirota bilinear method [1], the improved tan(φ(ξ )/ )-expansion method [3], the extended transformed rational function
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