In this paper we study the noncommutative extension of a modified U(n) sigma model in 2 + 1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U(3) solitons and consid...

We demonstrate self-similar evolution of fundamental and higher-order dark soliton stripes on a paraboloidal background in a bulk graded-index waveguide with self-defocusing nonlinearity. The results show that the dark soliton stripes can self-similarly evolve on the paraboloidal background when they pass through the nonlinear well or barrier, and their evolutions may lead to the generation of ...

A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be v...

Exciton effects on conjugated polymers are investigated in the soliton lattice system. We use the Su-Schrieffer-Heeger model with long-range Coulomb interactions treated by the single-excitation configuration-interaction method. The soliton band is present in the Peierls gap of the doped system. There appears a new kind of the exciton where an electron-hole pair is excited between the soliton b...

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the co...

We consider an integrable conformally invariant two dimensional model associated to the affine Kac-Moody algebra sl 3 (C). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U (1) vector...

At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of ...

We present a numerical study of interactions between dispersive waves (DWs) and solitons during supercontinuum generation in photonic crystal fibers pumped with picosecond laser pulses. We show how the soliton-induced trapping potential evolves along the fiber and affects the dynamics of a DW-soliton pair. Individual frequency components of the DW periodically interact with the soliton resultin...

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m, n) equation. Furthermore for the mixed models of linear and nonli...

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a ...