Related papers: A scattering theory of ultrarelativistic solitons
We derive a closed-form expression for the phase shift experienced by 1+1 dimensional kinks colliding at ultra-relativistic velocities (gamma v >> 1), valid for arbitrary periodic potentials. Our closed-form expression is the leading order…
In this short note we investigate the ultra-relativistic collisions of small amplitude oscillons in 1+1 dimensions. Using the amplitude of the oscillons and the inverse relativistic boost factor $\gamma^{-1}$ as the perturbation variables,…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
We study scattering of quasi one-dimensional matter-waves at an interface of two spatial domains, one with repulsive and one with attractive interatomic interactions. It is shown that the incidence of a Gaussian wavepacket from the…
Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass…
We investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent…
Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
The ultrarelativistic limit of the Kerr - Newman geometry is studied in detail. We find the gravitational shock wave background associated with this limit. We study the scattering of scalar fields in the gravitational shock wave geometries…
We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincar\'e, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit…
It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of…
By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii…
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 consider the interaction of two-component bright-bright solitons with a narrow potential barrier (splitter) in the framework of a system of two Gross-Pitaevskii (nonlinear-Schr\"{o}dinger) equations modeling a binary Bose-Einstein…
We present a new family of exact solutions of the Einstein equations, constructed through the Khan-Penrose procedure, that may be interpreted as representing the propagation of a pair of solitons, in the background of a plane-wave collision…