Abstract
In this paper, by using the extended direct
algebraic method, we obtain the exact traveling wave solutions for the
Kawachara equation and the modified Kawachara equation. The exact solutions of
the Kawachara and modified Kawachara equations demonstrated by graphs. The
stability of these solutions and the movement role of the waves by sketching
the graphs of the exact solutions are analyzed.
Keywords
Traveling wave solutions Extended direct algebraic method Kawachara equation modified Kawachara equation
References
- [1] Gubernov, V. et al., Numerical methods for the travelling wave solutions in reaction-diffusion equations, ANZIAM J. 44 (E) (2003), pp.C271-C289. [2] Ndeffo Mbah, M.L., Travelling wave solutions for PDEs, African Institute for Mathematical Sciences, Cape Town South Africa June 7 (2005), pp. 1-34. [3] Fan, E., Hon Y.C., A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves, Chaos, Solitons and Fractals 15 (2003), pp. 559-566. [4] Helal, M.A., Soliton solutions of some nonlinear partial differential equations and its applications in fluids mechanics, Chaos, Solitons and Fractals 13 (2002), pp.1917-1929. [5] Seadawy, A. R., Lu, D., Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability, Results in Physics 7 (2017), pp. 43-48. [6] Seadawy, A. R. et al., Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability, J. of Taibah University for Science 11(2017), pp. 623-633. [7] Seadawy, A. R., Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acustic waves in a plasma, Computers and Mathematics with Applications 67 (2014), pp. 172-180. [8] Arshad, M. et al., Travelling wave solutions of Drinfel’d-Sokolov-Wilson, Whitham-Broer-Kaup and (2+1)-dimensional Broer-Kaup-Kupershmit equations and their applications, Chinese Journal of Physics 55 (2017), pp. 780-797. [9] Kudryashov, N.A., On types of nonlinear nonintegrable equations with exact solutions, Physics Letters A 155 (1991), pp. 269-275. [10] Ertas, A., Mızrak, M., Explicit Travelling Wave Solutions of Two Nonlinear Evolution Equations, Mathematical Sciences Letters 3(3) (2014), pp. 223-228.
Abstract
References
- [1] Gubernov, V. et al., Numerical methods for the travelling wave solutions in reaction-diffusion equations, ANZIAM J. 44 (E) (2003), pp.C271-C289. [2] Ndeffo Mbah, M.L., Travelling wave solutions for PDEs, African Institute for Mathematical Sciences, Cape Town South Africa June 7 (2005), pp. 1-34. [3] Fan, E., Hon Y.C., A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves, Chaos, Solitons and Fractals 15 (2003), pp. 559-566. [4] Helal, M.A., Soliton solutions of some nonlinear partial differential equations and its applications in fluids mechanics, Chaos, Solitons and Fractals 13 (2002), pp.1917-1929. [5] Seadawy, A. R., Lu, D., Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability, Results in Physics 7 (2017), pp. 43-48. [6] Seadawy, A. R. et al., Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability, J. of Taibah University for Science 11(2017), pp. 623-633. [7] Seadawy, A. R., Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acustic waves in a plasma, Computers and Mathematics with Applications 67 (2014), pp. 172-180. [8] Arshad, M. et al., Travelling wave solutions of Drinfel’d-Sokolov-Wilson, Whitham-Broer-Kaup and (2+1)-dimensional Broer-Kaup-Kupershmit equations and their applications, Chinese Journal of Physics 55 (2017), pp. 780-797. [9] Kudryashov, N.A., On types of nonlinear nonintegrable equations with exact solutions, Physics Letters A 155 (1991), pp. 269-275. [10] Ertas, A., Mızrak, M., Explicit Travelling Wave Solutions of Two Nonlinear Evolution Equations, Mathematical Sciences Letters 3(3) (2014), pp. 223-228.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Submission Date | December 20, 2017 |
| Acceptance Date | March 28, 2018 |
| Publication Date | June 4, 2018 |
| Published in Issue | Year 2018 Volume: 4 Issue: 1 |
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
