classification of bounded travelling wave solutions of the generalized zakharov equation

Classification of bounded travelling wave solutions of the generalized Zakharov equation

By using bifurcation theory of planar ordinary differential‎ ‎equations all different bounded travelling wave solutions of the‎ ‎Generalized Zakharov equation are classified in different‎ ‎parametric regions‎. ‎In each of these parametric regions‎ ‎the exact explicit parametric‎ representation of all solitary‎, ‎kink (anti kink) and‎ ‎periodic wave solutions as well as their numerical simulatio...

Exact Travelling Wave Solutions for a Modified Zakharov–Kuznetsov Equation

The modied Zakharov–Kuznetsov (mZK) equation, ut + uux + uxxx + uxyy = 0, (1) represents an anisotropic two-dimensional generalization of the Korteweg–de Vries equation and can be derived in a magnetized plasma for small amplitude Alfvén waves at a critical angle to the undisturbed magnetic field, and has been studied by many authors because of its importance [1–5]. However, Eq. (1) possesses m...

Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

A class of particular travelling wave solutions of the generalized Benjamin-BonaMahony equation are studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered. Pacs:05.45.Yv, 52.35.Mw, 52.35.Sb, 02.30.Jr

Bounded travelling wave solutions for a modified form of generalized Degasperis-Procesi equation

In this paper, a modified form of generalized Degasperis–Procesi equation is studied by using the bifurcation theory and by the method of phase portraits analysis. Some bounded travelling waves (loop solitons, peakons, solitary waves and periodic waves) are found. Under different parameter conditions, exact parametric representations of the above travelling waves in explicit form and in implici...

Dynamical Behaviors and New Exact Bounded Travelling Wave Solutions for the Modified Degasperis-Procesi Equation

In this paper, we consider the modified Degasperis-Procesi equation ut − uxxt + 4uux = 3uxuxx + uuxxx by the theory of planar dynamical systems and qualitative theory of polynomial differential system. For three special cases, dynamical behaviors are investigated based on an independent variable transformation, and some new exact peakon, solitary wave, periodic wave and periodic cusp wave solut...

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation