We report on the experimental evidence of four wave mixing (FWM) between the two polarization components of a vector soliton formed in a passively mode-locked fiber laser. Extra spectral sidebands with out-of-phase intensity variation between the polarization resolved soliton spectra was firstly observed, which was identified to be caused by the energy exchange between the two soliton polarizat...

Depletion of soliton energy by four-wave mixing between a soliton and amplifier noise in a system with 100-km amplifier spacing is studied. Dispersion exponentially decreasing fiber is used as transmission fiber. Improvement of the system by the use of a sliding-frequency filter to reduce noise power and the depletion of soliton energy is shown. The system can be further improved by compensatio...

We study optical solitons in chirped periodic optical lattices whose amplitude or frequency changes in the transverse direction. We discover that soliton propagation in such lattices can be accompanied by the progressive self-bending of the soliton trajectory, and we show that the soliton bending rate and output position can be controlled by varying the lattice depth, as well as the chirp ampli...

We present the first experimental demonstration (to our knowledge) of long-distance unperturbed fundamental optical soliton transmission in conventional single-mode optical fiber. The virtual transparency in the fiber required for soliton transmission, over 15 complete periods, was achieved by using an ultralong Raman fiber laser amplification scheme. Optical soliton pulse duration, pulse bandw...

At low temperature, a quasi-one-dimensional ensemble of atoms with an attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass motion is affected. We show that in a spatially correlated disordered potential, the quantum motion of a bright soliton displays Anderson localization. The lo...

The purpose of this paper is to introduce the Ricci Yang-Mills soliton equations on nilpotent Lie groups. In the 2-step nilpotent setting, we show that these equations are strictly weaker than the Ricci soliton equations. Using techniques from Geometric Invariant Theory, we develop a procedure to build many different kinds of Ricci Yang-Mills solitons. We finish this note by producing examples ...

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 study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-solito...

Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered...

where λ is the soliton constant. In [2], Lauret proves the existence of many left invariant Ricci solitons on nilpotent Lie groups. The first explicit construction of Lauret solitons has been obtained by Baird and Danielo in [4]. In particular they show that the soliton structure on Nil is of nongradient type. Remarkably this is the first example of nongradient Ricci soliton. In [5], it is prov...