Related papers: Static multi-soliton solutions in the affine su(N+…
Solitonic objects play a central role in gauge and string theory (as, e.g., monopoles, black holes, D-branes, etc.). Certain string backgrounds produce a noncommutative deformation of the low-energy effective field theory, which allows for…
We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady…
Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation…
The new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are represented in explicit form. Soliton like solutions of them are represented…
We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space…
We prove the existence of multi-soliton solutions for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential and $L^2$-supercritical focusing nonlinear term. Our main contribution is to treat the unmoving part of the…
We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…
Contrary to the decades-old understanding, SGn, the Sine-Gordon equation in (1+n) dimensions, has N-soliton solutions for any N >= 1, not only for n = 1, but also for n = 2 and 3. While SG1 solitons are confined to a line, SG2- and…
A connection between differential geometry and soliton equations is discussed
All supersymmetric generalizations of the Standard Model allow for stable non-topological solitons of the Q-ball type which may have non-zero baryon and lepton numbers, as well as the electric charge. These solitons can be produced in the…
We discuss the structure of topological solitons in a general non-Heisenberg model of isotropic two-dimensional magnet with spin S=1, in the vicinity of a special point where the model symmetry is enhanced to SU(3). It is shown that upon…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…
This paper is concerned with the generalized Davey-Stewarston system in two dimensional space. Existence and stability of small solitons are proved by solving two correlative constrained variational problems and spectrum analysis. In…
In two space-time dimensions a class of classical multicomponent scalar field theories with discrete, in general non-Abelian global symmetry is considered. The corresponding soliton solutions are given for the cases of 2, 3, and 4…
We present a detailed analysis of the classical Dicke-Jaynes-Cummings-Gaudin integrable model, which describes a system of $n$ spins coupled to a single harmonic oscillator. We focus on the singularities of the vector-valued moment map…
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called…
We demonstrate that a staggered parametric ac driving term can support stable progressive motion of a soliton in a Toda lattice with friction, while an unstaggered drivng force cannot. A physical context of the model is that of a chain of…