Journal ArticleDOI
Exact solutions for the ZK-MEW equation by using the tanh and sine–cosine methods
TLDR
The tanh and sine–cosine methods are used to handle the two-dimensional ZK-modified equal-width equation (ZK-MEW) and reveal a number of useful features of the methods applied.Abstract:
The tanh and sine–cosine methods are used to handle the two-dimensional ZK-modified equal-width equation (ZK-MEW). The two methods work well to obtain exact solutions of different physical structures; solitary wave solutions and periodic solutions are also obtained. The framework presented here reveals a number of useful features of the methods applied.read more
Citations
More filters
Journal ArticleDOI
Travelling wave solutions of nonlinear evolution equations by using the first integral method
TL;DR: In this article, the first integral method was used to construct travelling wave solutions of nonlinear evolution equations, expressed by the hyperbolic functions, the trigonometric functions and the rational functions.
Journal ArticleDOI
Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine–cosine method
Elçin Yusufoğlu,Ahmet Bekir +1 more
TL;DR: The sine–cosine method is used to construct exact periodic and soliton solutions of coupled nonlinear evolution equations and many new families of exact travelling wave solutions of the Konopelchenko–Dubrovsky equations and the coupled non linear Klein–Gordon and Nizhnik–Novikov–Veselov equations are successfully obtained.
Journal ArticleDOI
Exact solutions of the (2+1 )-dimensional Zakharov-Kuznetsov modified equal width equation using Lie group analysis
TL;DR: The Lie group analysis is used to carry out the integration of the Zakharov-Kuznetsov modified equal width equation and the solutions obtained include the topological, non-topological soliton solution, cnoidal waves and the traveling wave solutions.
Journal ArticleDOI
Solutions and conservation laws of Benjamin–Bona–Mahony–Peregrine equation with power-law and dual power-law nonlinearities
TL;DR: In this paper, exact solutions of the Benjamin-Bona-Mahony-Peregrine equation with power-law and dual-power-law nonlinearities were obtained using the Lie group analysis and the simplest equation method.
Journal ArticleDOI
A procedure to construct exact solutions of nonlinear evolution equations
TL;DR: In this article, the functional variable method was used for exact solutions of the Zakharov-Kuznetsov modified equal width (ZK-MEW), the modified Benjamin-Bona-Mahony (mBBM) and the modified KdV-Kadomtsev-Petviashvili (KdV)-KP) equations.
References
More filters
Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Journal ArticleDOI
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Journal ArticleDOI
Solitary wave solutions of nonlinear wave equations
TL;DR: In this article, a method for obtaining traveling-wave solutions of nonlinear wave equations that are essentially of a localized nature is proposed based on the fact that most solutions are functions of a hyperbolic tangent.
Book ChapterDOI
Solitons, Nonlinear Evolution Equations and Inverse Scattering: References
M. A. Ablowitz,Peter A. Clarkson +1 more
Journal ArticleDOI
Compactons: Solitons with finite wavelength.
TL;DR: The behavior and the stability of these compactons is very similar to that observed in completely integrable systems.
Related Papers (5)
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more