We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial homogeneous gradient Ricci solitons. Thus the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the main result in [12] to show that there are no noncompact cohomogeneity one s...

We shall establish the existence and non existence of solitons (travelling waves of finite energy) for a Benney-Luke equation of higher order, which includes models for long water waves with small amplitude. Following a variational approach, solitons are characterized as critical points of the action functional. Existence of solitons follows by the ConcentrationCompactness principle by P.-L. Li...

We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We f...

We present both experimental and theoretical results on discrete solitons in two-dimensional optically-induced photonic lattices in a variety of settings, including fundamental discrete solitons, vector-like discrete solitons, discrete dipole solitons, and discrete soliton trains. In each case, a clear transition from two-dimensional discrete diffraction to discrete trapping is demonstrated wit...

We study the self-trapping of the superposition of two-dimensional vector dipole solitons in nonlocal media with an arbitrary degree of nonlocality. We apply the variational approach to find the exact solution of such vector dipole solitons and investigate their stability by using directly numerical simulations. The dynamics of such vector solitons are also compared with a scalar vortex. We sho...

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as (1+|r|(α)) support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionali...

Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities and stability of the solitons with respect to thermal...

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavio...

We report experimental studies of spatial optical solitons in a nonlinear glass waveguide. Spatial solitons are self-trapped beams that propagate without diffraction. We demonstrate the formation of spatial solitons, and we investigate interactions between them. At high intensities two-photon absorption is observed to lead to the breakup of solitons. A beam propagation method is used to simulat...

We study the finite θ correction to the metric of the moduli space of noncommutative multi-solitons in scalar field theory in (2+1) dimensions. By solving the equation of motion up to order O(θ−2) explicitly, we show that the multi-soliton solution must have the same center for a generic potential term. We examine the condition that the multi-centered configurations are allowed. Under this cond...