Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 37, Issue 3, Pages 3208-3225Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-017-0508-z
Keywords
ZK-MEW equation; Traveling wave solution; Kink-type solution; Weierstrass P function; Jacobi elliptic function; Dynamical systems; Theory of bifurcation
Categories
Ask authors/readers for more resources
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 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available