This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to ...

This paper studies the phi-four equation that arises in Quantum Mechanics. The topological 1-soliton solution or kink solution is obtained by the ansatz method. The bifurcation analysis is then subsequently carried out and several other solutions are retrieved from the analysis. These solutions include the solitary wave solutions, periodic waves and periodic singular waves. The constraint condi...

In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the traveling wave solutions of a 2-component of the Degasperis-Procesi equation. The expressions for smooth soliton, kink and antikink solutions are obtained.

We have studied the formation of relativistic solitary waves due to nonlinearinteraction of strong electromagnetic wave with the plasma wave. Here, our plasma isrelativistic both in temperature and in streaming speed. A set of equations consisting ofscalar and vector potentials together with a third order equation for the enthalpy inphoton gas plasma is obtained analytic...

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward. Keywords—Soliton solution, Computerized symbolic computation, Painlevé analysis, (2+1)-dimensional breaking ...

In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota’s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations. Keywords—(3+1)-dimensional breaking soliton equation, Hirota’s bilinear form.

The transformation of a weakly nonlinear interfacial solitary wave in an ideal twolayer flow over a step is studied. In the vicinity of the step the wave transformation is described in the framework of the linear theory of long interfacial waves, and the coefficients of wave reflection and transmission are calculated. A strong transformation arises for propagation into shallower water, but a we...

By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, t...