We analyze spatiotemporal dissipative solitons in two-dimensional photonic lattices in the presence of gain and loss. In the framework of the continuous-discrete cubic-quintic Ginzburg-Landau model, we demonstrate the existence of novel classes of two-dimensional spatiotemporal dissipative lattice solitons, which also include surface solitons located in the corners or at the edges of the trunca...

We report on the existence of surface defect gap solitons. Such new type of solitons can be well supported by an interface between the defect of optical lattice and the uniform media with focusing saturable nonlinearity. The surface defect of optical lattice can profoundly affect the properties of solitons. It is shown that for the positive defect, stable solitons exist at the first bandgap and...

We apply the Green’s function method to determine the global degree of squeezing and the transverse spatial distribution of quantum fluctuations of solitons in Kerr media. We show that both scalar bright solitons and multimode vector solitons experience strong squeezing on the optimal quadrature. For vector solitons, this squeezing is shown to result from an almost perfect anti-correlation betw...

We address the existence and properties of one-dimensional solitons maintained by localized parametric gain in focusing and defocusing lossy nonlinear media. Localized parametric gain supports both fundamental and multipole solitons. We found that the family of fundamental solitons is partly stable in focusing nonlinear medium, and completely stable in defocusing medium, while all higher-order ...

-Spatial dark solitons are known to be stable nonlinear localized waves in self-defocusing media. We demonstrate how to analyse the dynamics of dark solitons in the presence of small perturbations, and we consider the effect of two-photon absorption on dark solitons as a particular example. We also predict a new type of dark solitons of circular symmetry, ring dark solitons, which are stable ag...

We theoretically examine the interaction between two solitons in a double-mode optical fiber. The bound state between two solitons of different modes is investigated, including both dark and bright solitons. It is shown that interaction between dark solitons as well as between bright solitons is always attractive, but the interaction between bright and dark solitons may be repulsive. Analytical...

Collision of moving solitons is an interesting phenomena which is closely related to the stability of solitons. We study the head-on collision of solitons in a recently introduced model for biomembranes and nerves. We conduct simulations for pairs of solitons moving in opposite directions with the same velocity. It is found that these stable solitons collide elastically and it results a small a...

In J. Phys. Soc. Jpn. 83, 034404 (2014), we designed a scheme of waveguide arrays with long-range linear coupling effects and studied the bright solitons in this system. In this paper, we further study the dynamics of dark and grey solitons in such waveguide arrays. The numerical simulations show that the stabilities of dark solitons and grey solitons depend on the normalized decay length and t...

N-dark–dark solitons in the integrable coupled NLS equations are derived by the KP-hierarchy reduction method. These solitons exist when nonlinearities are all defocusing, or both focusing and defocusing nonlinearities are mixed. When these solitons collide with each other, energies in both components of the solitons completely transmit through. This behavior contrasts collisions of bright–brig...