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ON LOCALLY CONFORMALLY FLAT GRADIENT SHRINKING RICCI SOLITONS
SHRINKING RICCI SOLITONS CONFORMALLY FLAT
2015/8/17
In this paper, we first apply an integral identity on Ricci solitons to prove that
closed locally conformally flat gradient Ricci solitons are of constant sectional curvature.
We then ge...
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Hylomorphic solitons and their dynamics.
Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
Stability in two-dimensional discrete nonlinear schrodinger equation lattice discrete soliton
2014/12/29
We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation on two-dimensional nonsquare lattices. The model includes both the nearest-neighbor and lon...
Ring dark solitons and vortex necklaces in Bose-Einstein condensates
Dark soliton condensate cluster vortex pair oscillation
2014/12/29
We introduce the concept of ring dark solitons in Bose-Einstein condensates. We show that relatively shallow rings are not subject to the snake instability, but a deeper ring splits into a robust ring...
Averaging for Solitons with Nonlinearity Management
Average method of nonlinear schrodinger equation the soliton periodic variation nonlinear coefficient and condensate
2014/12/29
We develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Eins...
Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice
Dark soliton stability bose-einstein condensate magnetic parabolic well optical lattice discrete nonlinear schrodinger equation
2014/12/29
We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis ...
Discrete gap solitons in a diffraction-managed waveguide array
Model coupling nonlinear discrete diffraction optical waveguide array,
2014/12/29
A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. In the case of the cubic [ χ(3...
Dark-in-bright solitons in Bose-Einstein condensates with attractive interactions
Condensate the scattering length in the form of a dark soliton optical lattice parabolic magnetic trap discrete nonlinear schrodinger equation
2014/12/29
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an...
Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons
Nonlinear excited state dynamics bose gas five non-linear dynamic
2014/12/29
The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau regime with longitudinal confinement are studied within a mean-field theory of quintic nonlinearity. A reductive p...
Oscillations of dark solitons in trapped Bose-Einstein condensates
Oscillation parabolic equation the dark soliton amplitude attenuation radiation dark soliton
2014/12/29
We consider a one-dimensional defocusing Gross–Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative...
Stability of discrete solitons in nonlinear Schrödinger lattices
Discrete soliton bifurcate discrete nonlinear schrodinger lattice discrete soliton
2014/12/29
We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arb...
Statics, dynamics, and manipulations of bright matter-wave solitons in optical lattices
Condensate similar soliton parabolic magnetic trap periodic optical lattice space
2014/12/29
Motivated by the recent experimental achievements in the work with Bose-Einstein condensates (BECs), we consider bright matter-wave solitons, in the presence of a parabolic magnetic trap and a spatial...
Discrete solitons and vortices on anisotropic lattices
The two-dimensional nonlinear lattice discrete nonlinear schrodinger equation the vortex solitons
2014/12/25
We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental so...
Trapped bright matter-wave solitons in the presence of localized inhomogeneities
Solitary wave dynamics condensate power soliton dynamics
2014/12/25
We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized “impurity” in Bose–Einstein condensates (BECs). We study the generation and stability of a pair...