We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration,...

This paper deals with the transmission of a soliton in a discrete, nonlinear, and random medium. A random lattice nonlinear Schrödinger equation is considered, where the randomness holds in the on-site potential or in the coupling coefficients. We study the interplay of nonlinearity, randomness, and discreteness. We derive effective evolution equations for the soliton parameters by applying a p...

Soliton solutions of the perturbedLandau-Lifshitz equation, S t = [S × Sxx ] + [S × JS] + ER(S), c being a small parameter, describing the nonlinear dynamics of the magnetization field in a one-dimensional ferromagnet with a biaxial anisotropy, are analysed. Perturbation theory based on the Riemarm problem is constructed for studying the influence of small perturbations on the dynamics of domai...

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though the noise is weak, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approxim...

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as ...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

The NLSE soliton scattering by impurities is considered in the framework of the one-dimensional model. The scattering intensity is characterized by the reflection coefficient. The reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory for the following cases: (i) and isolated impurity, (ii) two point impurities, and (iii) a regular or random sys...

The intra-channel collision of optical solitons, with non-Kerr law nonlinearities, is studied in this paper by the aid of quasi-particle theory. The perturbations terms that are considered in this paper are both of Hamiltonian as well as nonHamiltonian type. The suppression of soliton–soliton interaction, in presence of these perturbation terms, is achieved. The nonlinearities that are studied ...

We investigate the interface coupling between the 2D sine-Gordon equation and the 2D wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effecti...

The perturbation theory based on the Riemann-Hilbert problem is constructed for the nonlinear Schrödinger equation. The second-order equations for the spectral data describing the soliton-wave interaction are obtained. The theory is applied to the parametrically driven, damped nonlinear Schrödinger equation. The parametrically driven NLS soliton is shown to become unstable, when the driving str...