This Letter reports experimental results on random temporal dark solitons. One excites an incoherent large-amplitude propagating spin-wave packet in a ferromagnetic film strip with a repulsive, instantaneous nonlinearity. One then observes the random formation of dark solitons from this wave packet. The solitons appear randomly in time and in position relative to the entire wave packet. They ca...

Einstein manifolds are trivial examples of gradient Ricci solitons with constant potential function and thus they are called trivial Ricci solitons. In this paper, we prove two characterizations of compact shrinking trivial Ricci solitons. M.S.C. 2010: 53C25.

Two-dimensional surface solitons have been recently predicted to exist as novel types of discrete solitons localized in the corners or at the edges of two-dimensional photonic lattices. These theoretical predictions were followed by the experimental observation of twodimensional surface solitons in optically-induced photonic lattices and waveguide arrays laser-written in fused silica. Important...

We describe a new algebraically completely integrable system, whose integral manifolds are co-elliptic subvarieties of Jacobian varieties. This is a multi-periodic extension of the Krichever-Treibich-Verdier system, which consists of elliptic solitons. The goal of this work is to generalize the theory of elliptic solitons, which was developed by A. Treibich and J.-L. Verdier based on earlier wo...

This Letter deals with topological solitons in an O(3) sigma model in three space dimensions (with a Skyrme term to stabilize their size). The solitons are classified topologically by their Hopf number N. The N = 2 sector is studied; in particular, for two solitons far apart, there are three " attractive channels ". Viewing the solitons as dipole pairs enables one to predict the force between t...

We experimentally investigated the vector multi-soliton operation and vector soliton interaction in an erbium doped fiber laser passively mode locked by atomic layer graphene. It is found that the vector multi-soliton operation exhibited several characteristic modes. These are the random static distribution of vector solitons, stable bunches of vector solitons, restless oscillations of vector s...

We present a detailed numerical study of creeping solitons in dissipative systems. A bifurcation diagram has been constructed for the region of transition between solitons and fronts. It shows a rich variety of transitions between various types of localized solutions. For the first time, we have found a sequence of period-doubling bifurcations of creeping solitons, and also a symmetry-breaking ...

We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional int...

We demonstrate that optical discrete solitons are possible in appropriately oriented biased photorefractive crystals. This can be accomplished in optically induced periodic waveguide lattices that are created via plane-wave interference. Our method paves the way towards the observation of entirely new families of discrete solitons. These include, for example, discrete solitons in two-dimensiona...