In this paper, by means of the general projective Riccati equation method (PREM), the variable separation solutions of the (2+1)-dimensional modified dispersive water-wave system are obtained. By further studying, we find that these variable separation solutions, which seem independent, actually depend on each other. Based on the special variable separation solution and choosing suitable functi...

Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation ~CGLE! are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable pulselike solutions of the quintic CGLE exis...

This paper obtains the exact 1-soliton solution of the perturbed Korteweg-de Vries equation with power law nonlinearity. The topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. It has been proved that topological solitons exist only when ...

The phenomenon of modulation instability of continuous-wave (cw) solutions of the cubic–quintic complex Ginzburg–Landau equation is studied. It is shown that low-amplitude cw solutions are always unstable. For higher-amplitude cw solutions, there are regions of stability and regions where the cw solutions are modulationally unstable. It is found that there is an indirect relation between the st...

This paper studies the Klein-Gordon equation with quadratic nonlinearity. The ansatz approach is used to first obtain the singular soliton solution of the equation along with the corresponding domain restriction. The bifurcation analysis is also carried out. By this analysis, a few more traveling wave solutions are retrieved. The bifurcation phase portraits are also given.

In this paper, the well-known He’s variational iteration method (VIM) is used to construct solitary wave solutions for the generalized Zakharov equation (GZE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure. c © 2007 Elsevier Ltd. All rights reserved.

Dust acoustic solitary waves are studied in warm dusty plasma containing negatively charged dusts, nonthermal ions and Boltzmann distributed electrons. Sagdeev pseudopotential method is used in order to investigate solitary wave solutions in the plasmas. The existence of compressive and rarefractive solitons is studied. Keywords—Nonthermal, Soliton, Dust, Sagdeev potential

We used what we called extended Fan’s sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson DS equations. The basic idea of the proposed extended Fan’s subequation method is to take fulls advantage of the general elliptic equations, involving five parameters, which have many new solutions and w...

In this paper we prove the soliton resolution conjecture for all times, solutions in energy space, of co-rotational wave map equation. To our knowledge is first such result initial data space a wave-type We also corresponding results radial solutions, which remain bounded norm, cubic (energy-critical) nonlinear equation dimension 4.

Based on a new first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term and some of its special solutions, a generalized transformation method is proposed to obtain more general exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky equations. As a result, new exact nontravelling wave solutions are obtained including soliton-like solutions and trigonomet...