相关论文: Numerical verification of a gap condition for line…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schr\"odinger equations with potentials. We show that the standing waves are orbitally stable for all frequencies in the $L^{2}$- subcritical and…
We study the long time behavior of small (in $l^2$) solutions of discrete nonlinear Schr\"odinger equations with potential. In particular, we are interested in the case that the corresponding discrete Schr\"odinger operator has exactly two…
We introduce a model based on a system of coupled nonlinear Schrodinger (NLS) equations with opposite signs infront of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a…
We consider a two-dimensional periodic Schr\"odinger operator $H=-\Delta+W$ with $\Gamma$ being the lattice of periods. We investigate the structure of the edges of open gaps in the spectrum of $H$. We show that under arbitrary small…
The purpose of this paper is to establish the existence and spectral stability, with respect to perturbations of the same period, of double-periodic standing waves for the nonlinear focusing Schr\"odinger equation posed on the…
This paper deals with the $L_p$-spectrum of Schr\"odinger operators on the hyperbolic plane. We establish Lieb-Thirring type inequalities for discrete eigenvalues and study their dependence on $p$. Some bounds on individual eigenvalues are…
We introduce and solve the one-dimensional quantum non-linear Schrodinger (NLS) equation for an N-component field defined on the real line with a defect sitting at the origin. The quantum solution is constructed using the quantum inverse…
We study the existence of standing waves, of prescribed $L^2$-norm (the mass), for the nonlinear Schr\"{o}dinger equation with mixed power nonlinearities $$ i \partial_t \phi + \Delta \phi + \mu \phi |\phi|^{q-2} + \phi |\phi|^{2^* - 2} =…
We analyze two-dimensional Schr\"odinger operators with the potential $|xy|^p - \lambda (x^2+y^2)^{p/(p+2)}$ where $p\ge 1$ and $\lambda\ge 0$, which exhibit an abrupt change of its spectral properties at a critical value of the coupling…
The paper deals with the existence of standing wave solutions for the Schr\"odinger-Poisson system with prescribed mass in dimension $N=2$. This leads to investigate the existence of normalized solutions for an integro-differential equation…
We consider a modulated discrete nonlinear Schr\"odinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a 'forbidden' gap. Nonlinear localized time-periodic solutions with…
In the space $L_2(R^d)$ we consider the Schr\"odinger operator $H_\gamma=-\Delta+ V(x)\cdot+\gamma W(x)\cdot$, where $V(x)=V(x_1,x_2,\dots,x_d)$ is a periodic function with respect to all the variables, $\gamma$ is a small real coupling…
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first clarify the spectral stability of such solutions depending on…
We show that wave operators for three dimensional Schr\"odinger operators $H=-\Delta + V$ with threshold singularities are bounded in $L^1({\mathbb R}^3)$ if and only if zero energy resonances are absent from $H$ and the existence of zero…
We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schrodinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the…
We consider the focusing mass supercritical nonlinear Schr\"odinger equation with rotation \begin{equation*} iu_{t}=-\frac{1}{2}\Delta u+\frac{1}{2}V(x)u-|u|^{p-1}u+L_{\Omega}u,\quad (x,t)\in \mathbb{R}^{N}\times\mathbb{R}, \end{equation*}…
Let $(\lambda_-,\lambda_+)$ be a spectral gap of a periodic Schr\"odinger operator $A$ on the lattice ${\mathbb Z}^d$. Consider the operator $A(\alpha)=A-\alpha V$ where $V$ is a decaying positive potential on ${\mathbb Z}^d$. We study the…
We investigate standing waves with prescribed mass for a class of biharmonic Schrodinger equations with positive Laplacian dispersion in the Sobolev critical regime. By establishing novel energy inequalities and developing a direct…
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr\"odinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave…