We study the dynamics of a narrow bright soliton in a one-dimensional lattice of condensed attractive atoms when the soliton width is comparable to the lattice spacing. If a momentum is imprinted to a stationary state, the soliton can have oscillations around a site or it can undergo a random motion along the array. The motion is very sensitive to the atomic background distribution, and a therm...

We experimentally investigated the vector multi-soliton operation and vector soliton interaction in an erbium doped fiber laser passively mode locked by atomic layer graphene. It is found that the vector multi-soliton operation exhibited several characteristic modes. These are the random static distribution of vector solitons, stable bunches of vector solitons, restless oscillations of vector s...

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics pr...

We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensates BEC model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferroma...

Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between co-propagating solitons with small temporal and wavelengths separation. The mechanism of graduate acceleration of trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuu...

We show how to generate robust self-sustained clusters of soliton bullets-spatiotemporal (optical or matter-wave) solitons. The clusters carry an orbital angular momentum being supported by competing nonlinearities. The "atoms" forming the "molecule" are fully three-dimensional solitons linked via a staircaselike macroscopic phase. Recent progress in generating atomic-molecular coherent mixing ...

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, ...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota's bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...

We calculate the spin-polarizabilities of the nucleon by means of dispersion relation, where the pion photoproduction amplitude predicted by chiral soliton model is utilized. We consider the Nπ and ∆π channels in the pion-photoproduction amplitude, and also evaluate the contribution of the anomalous term of the π0γγ process. In a narrow decay-width limit of the ∆ particle the result coincides w...

In each dimension N ≥ 3 and for each real number λ ≥ 1, we construct a family of complete rotationally symmetric solutions to Ricci flow on R which encounter a global singularity at a finite time T . The singularity forms arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate (T − t)−(λ+1). Near the origin, blow-ups of such a solution converge uniformly to the Bryant soli...