Related papers: Solitons: Kinks, Collisions and Breathers
We compute semiclassical corrections to the energy density of kinks in $\phi^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions, using local and covariant renormalization techniques from quantum field theory in curved…
Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component…
We investigate the long-time dynamics of the Sine-Gordon (SG) model under a class of perturbations whose quantum field theoretic analog - via bosonization - corresponds to the massive Schwinger model describing 1+1D relativistic QED of…
We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit…
We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions…
We consider an extended model with two real scalar fields, $\phi(x,t)$ and $\chi(x,t)$. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the $\chi^4$ one. The fields mutually interact…
We study scattering properties of topological solitons in two classes of models, which are generalizations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on an integer…
We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is non-homogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which…
The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional…
We study kink-antikink scattering in the sine-Gordon model in the presence of interactions with an additional scalar field, $\psi$, that is in its quantum vacuum. In contrast to the classical scattering, now there is quantum radiation of…
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and…
A model of the optical media with a spatially structured Kerr nonlinearity is introduced. The nonlinearity strength is modulated by a set of singular peaks on top of a self-focusing or defocusing uniform background. The peaks may include a…
We study soliton solutions to the Klein-Gordon equation via Lie symmetries and the travelling-wave ansatz. It is shown, by taking a linear combination of the spatial and temporal Lie point symmetries, that soliton solutions naturally exist,…
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…
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 study the kink-antikink scattering within the double sine-Gordon model. In the numerical simulations we found a critical value $v_{cr}$ of the initial velocity $v_{in}$, which separates two different scenarios: at $v_{in}<v_{cr}$ the…
This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and antikinks, which are perhaps the simplest examples of…
This paper is concerned with a lattice model which is suited to square-rectangle transformations characterized by two strain components. The microscopic model involves nonlinear and competing interactions, which play a key role in the…
In this work we analyze the possibility that soliton dynamics in a simple nonlinear model allows functionally relevant predictions of the behaviour of DNA. This suggestion was first put forward by Salerno [Phys. Rev. A, vol. 44, p. 5292…