Yaroslav V Kartashov

..The generation of stable dispersive shock waves is possible only below certain critical defect strength...

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..Stable complexes with separated components may be built not only of fundamental solitons, but of multipoles, too...

..Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion...

..In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection...

..Such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. Above the critical value of the gain, symmetry breaking occurs and asymmetric dissipative solitons emerge...

..Thus, complete beam reflection may be achieved for a set of resonant modulation frequencies at which light tunneling between adjacent guides of modulated lattice is inhibited...

..Tunneling inhibition is almost perfect for strongly localized modes with propagation constants close to the gap center...

..In contrast, we reveal that periodic alternation of the thermo-optic coefficient in layered thermal media makes possible the stabilization of higher-order multipoles...

..We find that, under suitable spectral resonance conditions, small transverse soliton oscillations may get parametrically amplified...

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..We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by nonlinear lattices, provided that the nonlinearity exhibits saturation...

..The setting addressed is a semiconductor material with both Kerr and thermal nonlinearities illuminated by a pulse train with suitable pulse width and repetition rate...

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..This enables the localization of light in single waveguide despite the remarkable difference of corresponding local and global energy tunneling rates...

..Dipole solitons also feature symmetry breaking, but under defocusing nonlinearity...

..The domains of soliton existence depend on the transverse growth rate of the filling nonlinearity and nonlinearity of the core. Remarkably, solitons exist even when the core material is linear...

..Here we discuss the method and show several illustrative examples of its potential...

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..For off-diagonal disorder the localization degree of the intensity distributions monotonically grows with increasing disorder. In contrast, under appropriate conditions, increasing diagonal disorder may result in weaker localization...

..In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons...

..e., α>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough...

..As an illustrative example, here we show their potential for spatial soliton control. Complex networks consisting of several intersecting or joining stripe-like lattices suited to a particular application may also be constructed...

..Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots...

..Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles...

..The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption...

..The quasinondiffracting patterns open up a wealth of opportunities for the manipulation of matter and optical waves, colloidal and living particles, with applications in biophysics, and quantum, nonlinear and atom optics...

..One-hump and two-hump dissipative defect modes are obtained...

..One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value...

..Three-dimensional light bullets are shown to form at reduced energy levels, in settings where the dispersion would be far too weak to generate bullets in the absence of array...