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...

We consider a high-order nonlinear Schrödinger (HNLS) equation with thirdand fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and ...

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....

Via the semi-inverse method, variational principles are established for the Drinfeld-Sokolov-Wilson (DSW) equation. Based on the obtained variational formulations, exact solitary solution and exact singular periodic wave solution can be obtained using the variational approach.

The aim of the paper is to show that splitting of a waveguide leads to fission of bulk solitons in solids. We study the dynamics of a longitudinal bulk solitary wave in a delaminated, symmetric layered elastic bar. First, we consider a two-layered bar and assume that there is a perfect interface when x<0 and complete debonding (splitting) when x>0 , where the axis Ox is directed along the bar. ...

A spectral solution of the RLW equation based on collocation method using Chebyshev polynomials as a basis for the approximate solution is proposed. Test problems, including the motion of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be more accurate than previous ones. The interaction of solitary waves is used to discuss the effect of th...

We study the nonlinear dynamics of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence of this solution are derived. The stability ...