相关论文: On linear stability of crystals in the Schroedinge…

We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…

A space-periodic ground state is shown to exist for lattices of smeared ions in $\R^3$ coupled to the Schr\"odinger and scalar fields. The elementary cell is necessarily neutral. The 1D, 2D and 3D lattices in $\R^3$ are considered, and a…

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…

The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context…

Consider the H^{1/2}-critical Schroedinger equation with a cubic nonlinearity in R^3, i \partial_t \psi + \Delta \psi + |\psi|^2 \psi = 0. It admits an eight-dimensional manifold of periodic solutions called solitons e^{i(\Gamma + vx -…

We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters…

Recently we have derived an effective one-dimensional nonpolynomial Schr\"odinger equation (NPSE) [Phys. Rev. A {\bf 65}, 043614 (2002)] that accurately describes atomic Bose-Einstein condensates under transverse harmonic confinement. In…

The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…

We consider the 3D cubic nonlinear Schr\"odinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of global solutions to the time-dependent model can be described…

In this paper, we investigate a class of planar Schr\"{o}dinger-Poisson systems with critical exponential growth. We establish conditions for the local well-posedness of the Cauchy problem in the energy space, which seems innovative as it…

We study multiple-period Bloch states of a Bose-Einstein condensate with spatially periodic interactomic interaction. Solving the Gross-Pitaevskii equation for the continuum model, and also using a simplified discrete version of it, we…

This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schr\"odinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral…

We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for…

The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time…

We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…

We analyze a numerical instability that occurs in the well-known split-step Fourier method on the background of a soliton. This instability is found to be very sensitive to small changes of the parameters of both the numerical grid and the…

We study the following doubly critical Schr\"{o}dinger system $$-\Delta u -\frac{\la_1}{|x|^2}u=u^{2^\ast-1}+ \nu \al u^{\al-1}v^\bb, \quad x\in \RN, -\Delta v -\frac{\la_2}{|x|^2}v=v^{2^\ast-1} + \nu \bb u^{\al}v^{\bb-1}, \quad x\in \RN,…

We prove that twisting and filamentation occur near a family of stable steady states for one dimensional periodic Vlasov-Poisson system, describing the electron dynamics under a fixed ion background. More precisely, we establish the growth…

We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an…

We study the orbital stability and instability of single-spike bound states of semiclassical nonlinear Schrodinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs). These equations may model…