Related papers: Multi loop soliton solutions and their interaction…
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…
The splitting between the charge-longitudinal and spin-transverse responses is explained in a model whose inputs are the effective interactions in the particle-hole channels in the first order boson loop expansion. The interplay between…
We report for the first time exact solutions of a completely integrable nonlinear lattice system for which the dynamical variables satisfy a q-deformed Lie algebra - the Lie-Poisson algebra su_q(2). The system considered is a q-deformed…
We study the dynamics of multipulse solutions in mode-locked lasers in presence of time-delayed feedback stemming, e.g., from reflections upon optical elements, and carrier dynamics. We demonstrate that the dynamics of such a high…
Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified…
Dipolar interactions support the formation of inter-site soliton molecules in a stack of quasi-1D traps. We show that the stability and properties of individual solitons, and soliton molecules in such a geometry crucially depend on the…
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures [1]. The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a…
We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms,…
We consider certain degenerations of trigonal curves and hyperelliptic curves, which we call one step degeneration. We compute the limits of corresponding quasi-periodic solutions using the Sato Grassmannian. The mixing of solitons and…
We consider few problems which are related to the deuteron and have simple analytical solution. Relation is found between the deuteron electric quadrupole moment and the $np$-scattering amplitude. The degree of circular polarization of…
We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as $r^{-3}$, where $r$ is the interatomic separation. We supply an exact result for a single atom in a given state…
The peculiar intergrability of the Davey-Stewartson equation allows us to find analytically solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted…
Using loop equation technics, we compute all mixed traces correlation functions of the 2-matrix model to large N leading order. The solution turns out to be a sort of Bethe Ansatz, i.e. all correlation functions can be decomposed on…
We analyze soliton solutions in the duality-based matrix model. There are two types of solution, a one soliton-antisoliton solution (with the constant boundary condition at infinity) and a periodic solution with an infinite number of…
In this Letter we further develop the proposed approach of optical manipulation based on the interactions of non-linear optical effects with nanoparticles. The interaction of the dissipative optical solitons with nanoparticles is studied…
We propose a method of forming matter-wave soliton molecules that is inspired by the recent experiment of Dris {\it et al.}. In the proposed set-up we show that if two solitons are initially prepared in phase and with a sufficiently small…
In this paper, we use Hirota's bilinear method to directly construct periodic wave solutions of nonlinear equations. The asymptotic property of periodic wave solutions are analyzed. It is shown that well-known soliton solutions can be…
In this paper, we employ the bifurcation method of dynamical systems to investigate the exact travelling wave solutions for the Fornberg-Whitham equation. The implicit expression for solitons is given. The explicit expressions for peakons…