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Computational and Applied Mathematics

, Volume 37, Issue 3, pp 3208–3225 | Cite as

Explicit Weierstrass traveling wave solutions and bifurcation analysis for dissipative Zakharov–Kuznetsov modified equal width equation

  • Amiya Das
Article
  • 110 Downloads

Abstract

We consider the dissipative Zakharov–Kuznetsov modified equal width (ZK-MEW) equation and discuss the effect of the dissipation on the existence and nature of traveling wave solutions of the equation. We use Lyapunov function and dynamical system theory in order to show that when viscosity term is added to the ZK-MEW equation, yet there exists still bounded traveling wave solutions in certain regions. Subsequently, we obtain general solution of the ZK-MEW equation in the presence and absence of viscosity in terms of Weirstrass \(\wp \) functions and Jacobi elliptic functions. We also derive a new form of kink-type solution by exploring a factorization method based on functional transformation and the Abel’s first order nonlinear equation. Finally, we use the phase plane analysis and examine the stability of the viscous waves.

Keywords

ZK-MEW equation Traveling wave solution Kink-type solution Weierstrass \(\wp \) function Jacobi elliptic function Dynamical systems Theory of bifurcation 

Mathematics Subject Classification

37B55 34K18 35C07 35L67 33E05 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Department of MathematicsKazi Nazrul UniversityAsansolIndia

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