We study the finite θ correction to the metric of the moduli space of noncommutative multi-solitons in scalar field theory in (2+1) dimensions. By solving the equation of motion up to order O(θ−2) explicitly, we show that the multi-soliton solution must have the same center for a generic potential term. We examine the condition that the multi-centered configurations are allowed. Under this cond...

This paper summarizes some of the relevant features exhibited by bi-nary mixtures Bose-Einstein condensates in presence coherent coupling at zero temperature. The coupling, which is experimentally produced proper photon transitions, can either involve negligible momentum transfer from electromagnetic radiation (Rabi coupling) or large (Raman associated with spin-orbit effects.The nature quantum...

We investigate numerically the collision dynamics of elliptically polarized solitons of the System of Coupled Nonlinear chrödinger Equations (SCNLSE) for various different initial polarizations and phases. General initial elliptic polarizations (not ech-shape) include as particular cases the circular and linear polarizations. The elliptically polarized solitons are computed by separate numerica...

Complex (dusty) plasmas consist of micron sized microparticles immersed into ordinary ion-electron plasmas. They can exist in solid, liquid or gaseous states and exhibit a range of dynamic phenomena such as linear and nonlinear dust waves, solitons, shocks, Mach cones, heat transfer by phonons, flows, etc. We report on the experimental and numerical study of dissipative solitons in complex plas...

We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point, where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the sam...

We report on the observation of various bound states of dispersion-managed (DM) solitons in a passively mode-locked erbium-doped fiber ring laser at near zero net cavity group velocity dispersion (GVD). The generated DM solitons are characterized by their Gaussian-like spectral profile with no sidebands, which is distinct from those of the conventional solitons generated in fiber lasers with la...

We study the relationship between ADHM/Nahm construction and “solution generating technique” of BPS solitons in noncommutative gauge theories. ADHM/Nahm construction and “solution generating technique” are the most strong ways to construct exact BPS solitons. Localized solitons are the solitons which are generated by the “solution generating technique.” In “solution generating technique,” shift...

For the L subcritical and critical (gKdV) equations, Martel [11] proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of (gKdV) which behaves as the sum of these N solitons asymptotically as t → +∞. More recently, for the L supercritical case, Côte, Martel and Merle [4] proved the existence of at least one multi-soliton. I...

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of smal...

Several new nonlinear systems are given which are completely integrable. These systems can be considered as flows describing the self-interaction of single solitons in multisoliton fields. The construction of action variables, recursion operators, bi-hamiltonian formulation and the like is performed for these nonlinear systems. Furthermore virtual solitons are introduced and it is shown that 2-...