By means of the coupled amplitude-phase method we find analytical dark solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media. The dark solitary wave solution exists even for the coefficients of quintic terms much larger than...

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to the free Schrödinger equation. The proofs...

Using a variational approach we have studied the shape preserving coherent propagation of light pulses in a resonant dispersive medium in the presence of the Kerr nonlinearity. Within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations, we show the existence of a solitary wave. We have tested our analytical solution through numeri...

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...

We consider the stability of solitary waves of a class of 5th order KdV equations. It is known that their stability is determined by the second derivative of a function of the wave speed d(c). We perform a detailed investigation of the properties of this function, both analytically and numerically. For a class of homogeneous nonlinearities, we precisely determine the regions of wave speeds for ...

In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkabl...

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 ...

We introduce a new type of solitary wave in a lossless single-mode fiber in which a bright solitonlike pulse in the anomalous-dispersion range propagates together with a stationary dark pulse in the normal-dispersion range. Such a solitary wave can be generated by launching a bright pulse in the anomalous-dispersion range together with a long pulse of the same speed in the normal-dispersion ran...

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinea...

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum...