and hosti .2013.08.0 Abstract In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc.) envelope for the underst...

G 󸀠 /G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained.When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solution...

Abstract In this paper we consider a coupled KdV system of Boussinesq type and its symmetric version. These systems were previously shown to possess generalized solitary waves consisting of a solitary pulse that decays symmetrically to oscillations of small, constant amplitude. We solve numerically the periodic initial-value problem for these systems using a high order accurate, fully discrete,...

In this paper we consider a coupled KdV system of Boussinesq type and its symmetric version. These systems were previously shown to possess Generalized Solitary Waves consisting of a solitary pulse that decays symmetrically to oscilations of small, constant amplitude. We solve numerically the periodic initial-value problem for these systems using a high order accurate, fully discrete, Galerkin-...

Nonlinear Schrödinger equations (NLSs) with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary waves and to the long-time dynamics of solutions of NLSs. We study these spectra in detail, both analytically and numerically.

Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the reduced Ostrovsky equation. It is shown how the nature of the waves may be categorized in a simple way by considering the value of a certain single combination ...

It was shown in [1] that waves in a two-layer system with free-surface boundary conditions (or in a three-layer system) can be modelled by a system of two coupled long wave equations. The study of the resonance between a solitary wave of one of the two equations and a copropagating periodic wave of the other equation is carried out numerically. The resulting wave is a generalized solitary wave....

A generalized Fisher equation involving a nonlinear term of any order and timedependent coefficients is investigated. We present exact analytical solutions describing periodic and solitary wave solutions using the modified sine-cosine method. A certain class of exact soliton-like solutions has been found by means of the auxiliary equation method. The conditions of existence and uniqueness of th...

Long surface gravity waves of finite amplitude in uniform shear flows are considered by using an asymptotic model derived under the assumption that the aspect ratio between wavelength and water depth is small. Since its derivation requires no assumption on wave amplitude, the model can be used to describe arbitrary amplitude waves. It is shown that the simple model captures the interesting feat...

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support. This is the second in a series of two p...