the thomas-fermi (tf) equation has proved to beuseful for the treatment of many physical phenomena. in this pa-per, the traveling wave solutions of the kdv equation is investi-gated by the simplest equation method. also, the effect of differentparameters on these solitary waves is considered. the numericalresults is conformed the good accuracy of presented method.

In their proof of the stability of standing-wave solutions of nonlinear Schrödinger equations, Cazenave and Lions used the principle of concentration compactness to characterize the standing waves as solutions of a certain variational problem. In this article we first review the techniques introduced by Cazenave and Lions, and then discuss their application to solitary-wave solutions of nonloca...

In this paper, we use two different integral techniques, the first integral and the direct integral method, to study the variable coefficient nonlinear Schrödinger (NLS) equation arising in arterial mechanics. The application of the first integral method yielded periodic and solitary wave solutions. Using the direct integration lead to solitary wave solution and Jacobi elliptic function solutions.

We investigate how the non-analytic solitary wave solutions — peakons and compactons — of an integrable biHamiltonian system arising in fluid mechanics, can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system. This phenomenon is examined to understand the important effect of linear dispersion terms on the analyticity of...

We investigate how the non-analytic solitary wave solutions | peakons and compactons | of an integrable biHamiltonian system arising in uid mechanics, can be recovered as limits of classical solitary wave solutions forming analytic homoclinic orbits for the reduced dynamical system. This phenomenon is examined to understand the important eeect of linear dispersion terms on the analyticity of su...

In this research, we employ the extended exp(−φ(ξ))expansion method for the first time to obtain the exact and solitary wave solutions of the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation. We obtain the wide range of exact and solitary wave solutions of distinct physical structure.

A detailed mathematical analysis is undertaken of solitary wave solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with (2) nonlinearity. The so called bright-bright case is studied exclusively. The system depends on a single dimension-less parameter which includes both wave and material properties. Using variational methods, the rst rigoro...

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation is further investigated. By using the solutions of this equation, and a new general ansatz, we give some types of solutions of a class of nonlinear partial differential equations and MKdV equation. These solutions includes solitary wave solutions, singulary solitary solitary solutions...

Weakly nonlinear waves in elastic rods have been studied by many authors. Most studies concentrated on smooth solutions only. However, when waves are of moderate length, non-smooth waves, such as peakons (or solitary shock waves), can arise (see Dai and Huo 2000). For strongly nonlinear waves (not assuming the smallness of the wave amplitude), as far as the authors are aware, only incompressibl...

In this paper, the modified exp-function method is used to seek generalized wave solutions of Klein-Gordon equation. As a result, some new types of exact traveling wave solutions are obtained which include kink wave solutions, periodic wave solution, and solitary wave solutions. Obtained results clearly indicate the reliability and efficiency of the proposed modified exp-function method.