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-...

The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS in an external potential. A quantum lattice algorithm is developed fo...

In a space-time of two dimensions the overall effect of the collision of two solitons is a time delay (or advance) of their final trajectories relative to their initial trajectories. For the solitons of affine Toda field theories, the space-time displacement of the trajectories is proportional to the logarithm of a number X depending only on the species of the colliding solitons and their rapid...