The passive mode-locked fiber lasers are of great interest for a study of diversified features of a soliton dynamics. Dispersion parameters and a form of intensity-dependent nonlinear losses in the fiber lasers with nonlinear polarization rotation technique can be changed in a very large range that provides a distinct manifestation of varied soliton properties including a quantization of an int...

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

We investigate the propagation of a dark beam in a defocusing medium in the strong nonlinear regime. We observe for the first time a shock fan filled with noninteracting one-dimensional gray solitons that emanates from a gradient catastrophe developing around a null of the optical intensity. This scenario turns out to be very robust, persisting also when the material nonlocal response averages ...

We consider the interplay of repulsive short-range and same-sign long-range interactions in dynamics dark solitons, as prototypical coherent nonlinear excitations a trapped one-dimensional Bose gas. First, form ground state is examined, then both existence solitary waves their stability properties are explored, corroborated by direct numerical simulations. find that single- multiple-dark-solito...

There are periodic soliton resonances in interactions between two periodic solitons and between periodic soliton and another kind of soliton. A close relation exists between the periodic soliton resonance and soliton instability to transverse disturbances. It is shown that the instability occurred in the line soliton is relaxed by emission of the periodic soliton and the periodic soliton resona...

We have experimentally investigated the soliton interaction in a passively mode-locked fiber ring laser and revealed the existence of three types of strong soliton interaction: a global type of soliton interaction caused by the existence of unstable cw components, a local type of soliton interaction mediated through the radiative dispersive waves, and the direct soliton interaction. We found th...

We report what is to our knowledge the first observation of pixellike spatial solitons from partially spatially incoherent light. We created an array of as many as 32x32 soliton pixels by launching a spatially modulated incoherent light beam into a noninstantaneous self-focusing photorefraction medium. These solitons were stable and robust, forming a steady-state two-dimensional waveguide array...

Stable embedded solitons are discovered in the generalized third-order nonlinear Schrödinger equation. When this equation can be reduced to a perturbed complex modified Korteweg-de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numeric...

We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fu...

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order statistics is associated with certain constraints. In particular, we derive an inequality on distribution for related order statistics. Moreover, we also propos...