We report a novel spontaneous soliton pattern formation in a figure-of-eight passively mode-locked erbium-doped double-clad fiber laser. It consists in a condensate phase in which there is almost periodic arrangement of alternate crystal and liquid soliton phases. Thanks to an adapted ansatz for the electric field, we perform a reconstruction allowing to clearly identify the soliton distributio...

A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale perturbations can be taken and thus higher dimensional integrable couplings can be presented. The theory is applied to the KdV soliton hierarchy. Infinitely many ...

In this paper, we consider the characterization of eigenfunctions for Laplacian operators on some Riemannian manifolds. Firstly we prove that for the space form (M K , gK) with the constant sectional curvature K, the first eigenvalue of Laplacian operator λ1 (M K) is greater than the limit of the first Dirichlet eigenvalue of Laplacian operator λ1 (BK (p, r)). Based on this, we then present a c...

We investigate the various time-dependent bubble spacetimes that can be obtained from double analytic continuation of asymptotically locally flat/AdS spacetimes with NUT charge. We find different time-dependent explicit solutions of general relativity from double analytic continuations of Taub-Nut(AdS) and Kerr-Nut(AdS) spacetimes. One solution in particular has Milne-like evolution throughout,...

Using the quasi-particle approach, we studied the problem of the reflection of quadratic spatial solitons from an interface between two x (2) media with slightly different linear and nonlinear properties. The possibility of soliton capture by an interface associated with nonlinear surface wave excitation is shown. The calculations are carried out for the well-known single as well as a novel typ...

We provide analytical functions approximating e −x 2 dx, the basis of which is the kink soliton. Because of the accuracy and simplicity of the results (maximum error < 0.2%), it brings new hope that e −x 2 dx can in fact be written as the sum of simple analytical functions. We demonstrate our results with some applications, particularly to generation of Gaussian random fields without Monte Carl...

We prove that any gradient shrinking Ricci soliton has at most Euclidean volume growth. This improves a recent result of H.-D. Cao and D. Zhou by removing a condition on the growth of scalar curvature. A complete Riemannian manifold M of dimension n is called gradient shrinking Ricci soliton if there exists f ∈ C (M) and a constant ρ > 0 such that Rij +∇i∇jf = ρgij , where Rij denotes the Ricci...

DARK-BRIGHT SOLITONS AND VORTICES IN BOSE-EINSTEIN CONDENSATES MAY 2014 DONG YAN B.S., ZHEJIANG UNIVERSITY, CHINA M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Panayotis G. Kevrekidis This dissertation focuses on the properties of nonlinear waves in Bose-Einstein condensates (BECs). The fundamental model here is the nonlinear Schrödi...

We demonstrate an all-fiber-integrated Er-doped fiber laser operating in the soliton-similariton mode-locking regime. In the similariton part of the cavity, a self-similarly evolving parabolic pulse with highly linear chirp propagates in the presence of normal dispersion. Following an in-line fiber-based birefringent filter, the pulse evolves into a soliton in the part of the cavity with anomal...

We fully characterize the stationary spatial-gap soliton through the measurement of the phase function of its nearly periodic transverse intensity distribution. The spatial-gap soliton is generated in one-dimensional photonic crystal consisting of a corrugated semiconductor planar optical waveguide. The measured phase function allows us to determine the detuning parameter that provides the posi...