ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Algebraic Traveling Wave Solutions to Nonlinear Evolution Equations

Journal of Applied Nonlinear Dynamics 8(4) (2019) 557--567 | DOI:10.5890/JAND.2019.12.004

Yakup Yıldırım$^{1}$, Emrullah Yaşar$^{2}$

$^{1}$ Department of Mathematics, Faculty of Arts and Sciences, Near East University, 99138 Nicosia, Cyprus

$^{2}$ Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey

Abstract

In this paper, we employ planar dynamical systems and invariant algebraic curves to characterize all algebraic traveling wave solutions to nonlinear evolution equations. In order to demonstrate the applicability and efficiency of the method, we apply the approach to four (2+1)-dimensional integrable extensions of the Kadomtsev–Petviashvili equation. The numerical simulations are also plotted for better understanding the physical phenomena.

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