We realize an absolute position control of drifting dissipative optical solitons by injecting an incoherent amplitude parameter gradient onto the nonlinear optical system. This allows for two-dimensional, arbitrary control patterns. The control of the soliton drift velocity is studied applying a periodic, hexagonally shaped modulation. The guiding of dissipative solitons by one- and two-dimensi...

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. The...

This dissertation studies solitary waves in collisionally inhomogeneous BoseEinstein condensates in a magnetic trap using a quasi-1D mean-field model. We introduce a model for Bose-Einstein condensate with spatially and temporally modulated nonlinearity. In terms of the spatially periodic nonlinear lattice, we study BECs in a lattice one of which minimum in a period either overlap with the mini...

We characterize dark-type vector optical solitons of arbitrary polarization in isotropic, Kerr-type media by applying Hirota’s method to the integrable Manakov model with a defocusing nonlinearity. We find that nonuniformly polarized solitons comprise a rich solution family that can be divided into two categories: dark-dark and dark-bright vector solitons. We consider the propagation dynamics a...

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including one-dimensional fundamental and multihump states, two-dimensional vortex solitons with arbitrarily high t...

Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for solitons up to charge five the solutions have the structure of closed strings, which become increasingly twisted as the charge increases. However, for higher c...

We report a diversity of stable gap solitons in a spin-orbit-coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons can be classified by the main physical symmetries they obey, i.e., symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e., spin (C), inversions. The conventional gap and gap-stripe solitons are ob...

We discuss the creation of an array of 9 x 9 photorefractive spatial screening solitons in a strontium barium niobate crystal. We investigate the waveguide properties of each channel with a beam of different wavelength and find that the waveguides guide the probe beam independently. A supplementary beam is used to influence the paths of the array solitons and to effectively combine two channels...

In N(k)-contact metric manifolds and/or (k, μ)-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with V pointwise collinear with the structure vector field ξ are studied. Mathematics Subject Classification: 53C15, 53C25, 53A30.

Self-localized states or dissipative solitons have the freedom of translation in systems with a homogeneous background. When compared to cavity solitons in coherently driven nonlinear optical systems, laser cavity solitons have the additional freedom of the optical phase. We explore the consequences of this additional Goldstone mode and analyze experimentally and numerically frequency and phase...