相关论文: Continuum limit related to dispersion managed nonl…
We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators where the angular momentum takes the critical value $l=-\frac{1}{2}$. We also derive several new estimates for solutions of the underlying…
We consider the nonlinear Schr\"odinger equation$$-\Delta u + V(x)\,u = a\,u^p + \mu u \quad \text{in }\mathbb{R}^n,\qquad \int_{\mathbb{R}^n} u^2 = 1,$$modeling attractive Bose--Einstein condensates. For all dimensions $n\ge 2$ and all…
This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schr\"odinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation $i\partial _{t}u+\epsilon \Delta u+\delta A…
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that…
We study the discrete nonlinear Schr\"odinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective ''non-rigid pendulum'' Hamiltonian. The different regimes include the…
The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…
We investigate the well-posedness theory of the 2-D fractional nonlinear Schr\"odinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics where the light propagation is governed by non-quadratic,…
We consider numerical solution of Coupled Nonlinear Schr\"{o}dinger Equation. We prove stability and convergence in the $L_2$ space for an explicit scheme which estimations is used for implicit scheme and compare both method. As a test we…
We obtain global well-posedness, scattering, and global $L^{\frac{2(n+2)}{n-2}}_{t,x}$ spacetime bounds for energy-space solutions to the energy-critical nonlinear Schr\"odinger equation in $\R_t\times \R^n_x$, $n\geq 5$.
We consider the nonlinear Schrodinger equation with a logarithmic nonlinearity in a dispersive regime. We show that the presence of the nonlinearity affects the large time behavior of the solution: the dispersion is faster than usual by a…
We consider the problem of identifying sharp criteria under which radial $H^1$ (finite energy) solutions to the focusing 3d cubic nonlinear Schr\"odinger equation (NLS) $i\partial_t u + \Delta u + |u|^2u=0$ scatter, i.e. approach the…
We construct solutions of Schr\"odinger equations which are asymptotically self-similar solutions as time goes to infinity. Also included are situations with two bubbles. These solutions are global, with non-zero $L^2$ norms, and are…
We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Our construction starts with the existence of solution to the truncated subcritical problem.…
In this paper, we find normalized solutions to the following Schr\"{o}dinger equation \begin{equation}\notag \begin{aligned} &-\Delta u-\frac{\mu}{|x|^2}h(x)u+\lambda u =f(u)\quad\text{in}\quad\mathbb{R}^{N},\\ & u>0,\quad…
We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schr\"odinger equation with diffusive forcing.…
This paper is motivated by a gauged Schrodinger equation in dimension 2 including the so-called Chern-Simons term. The radially symmetric case leads to an elliptic problem with a nonlocal defocusing term, in competition with a local…
In this paper, we prove that there exists some small $\varepsilon_*>0$, such that the derivative nonlinear Schr\"{o}dinger equation (DNLS) is global well-posedness in the energy space, provided that the initial data $u_0\in H^1(\mathbb{R})$…
We consider large time asymptotics for damped nonlinear Schr\"{o}dinger equations. It is known that the nonlinear solution asymptotically behaves like a linear solution when time $t$ tends to infinity in the energy space. We prove that its…
The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical…