Related papers: Direct scattering transform: catch soliton if you …
We show the complete integrability and the existence of optical solitons of higher order nonlinear Schrodinger equation by inverse scattering method for a wide range of values of coefficients. This is achieved first by invoking a novel…
Interpretation of random wave field on a shallow water in terms of Fourier spectra is not adequate, when wave amplitudes are not infinitesimally small. A nonlinearity of wave fields leads to the harmonic interactions and random variation of…
We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the…
We investigate the validity of collective coordinate approaximations to the scattering of solitons in several classes of models in (1+1) dimensional field theory models. We look at models which are deformations of the sine-Gordon (SG) or…
We investigate a propagation of solitons for nonlinear Schr\"odinger equation under small driving force. The driving force passes through the resonance. The process of scattering on the resonance leads to changing of number of solitons.…
We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…
Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an…
In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schr\"odinger equations, which is a nonintegrable system…
In this paper, we study one-dimensional linear Schr\"odinger equations with multiple moving potentials, known as transfer charge models. Focusing on the non-self-adjoint setting that arises in the study of solitons, we systematically…
We have shown that the wave scattering by a soliton occurs in a peculiar way. The nonlinear interaction leads to the generation of waves with frequencies that are multiples of the frequency of the incident wave, minus the frequency of the…
We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…
We are interested in the scattering problem for the cubic 3D nonlinear defocusing Schr\"odinger equation with variable coefficients. Previous scattering results for such problems address only the cases with constant coefficients or assume…
In this paper, we study the direct and inverse scattering of the Schr\"odinger equation in a three-dimensional planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the…
We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…
In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and…
We study the non-equilibrium dynamics obtained by an abrupt change (a {\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\"odinger equation. We first consider explicit one-soliton examples, which we…
We investigate scattering properties of a Moyal deformed version of the nonlinear Schr\"odinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
We study the nonlinear Schr$\ddot{o}$dinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized…
A previous paper [J. Phys. B: At. Mol. Opt. Phys. 50, 215302 (2017)] showed that partial wave analysis becomes applicable to nonrelativistic Coulomb scattering if wavepackets are used. The scattering geometry considered was special: that of…