New exact solutions for the space-time fractional Kawahara equation
| Autor: | Sevil Çulha Ünal, Ayşegül Daşcıoğlu |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Partial differential equation
Applied Mathematics Space time Direct method Analytic Solutions Characteristic equation Duffing equation 02 engineering and technology Plasma 01 natural sciences Jacobi elliptic functions Jacobi elliptic function 020303 mechanical engineering & transports 0203 mechanical engineering Modeling and Simulation Kawahara equation Fractional partial differential equation Expansion Method 0103 physical sciences Applied mathematics Traveling-Wave Solutions Graphics 010301 acoustics Nonlinear differential equation Mathematics |
| Popis: | The Kawahara equation is a model of capillary-gravity water wave and plasma waves. In this paper, a direct method based on the Jacobi elliptic functions is presented to get analytical solutions of the space-time fractional Kawahara equation. Moreover, new exact solutions are obtained for a nonlinear ordinary differential equation (dF/d xi)(2) = PF4(xi) + QF(2)(xi) + R, which appears as an auxiliary equation for solving many partial differential equations. Some notes, theorems, and corollaries are also given for this equation. Solving this auxiliary equation, the solutions of the Duffing equation can also be found. Besides, three test examples are presented to illustrate the application of the method and some solutions are demonstrated by the graphics. (C) 2020 Elsevier Inc. All rights reserved. |
| Databáze: | OpenAIRE |
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