In this paper we investigate the properties of self induced transparency (SIT) solitons, propagating in a Λ-type medium. We find that the interaction between SIT solitons can lead to trapping with their phase preserved in the ground state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furt...

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 ...