Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics.
نویسنده
چکیده
We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.
منابع مشابه
Local Absorbing Boundary Conditions for a Finite Element Discretization of the Cubic Nonlinear Schrödinger Equation
We consider in this work the initial value problem for the one dimensional cubic nonlinear Schrödinger equation. In order to integrate it numerically, one option frequently used, is to impose local absorbing boundary conditions. A finite element discretization in space of the cubic nonlinear Schrödinger equation is considered along with the absorbing boundary conditions obtained for an analogou...
متن کاملAsymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals
This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using the Fokas’ transformation method, we show that for the linear Schrödin...
متن کاملAsymptotics of the heat equation with ‘exotic’ boundary conditions or with time dependent coefficients
The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and Dirichlet or Robin boundary conditions.
متن کامل2 00 3 The Forced Non - Linear Schrödinger Equation with a Potential on the Half - Line ∗ Ricardo Weder
In this paper we prove that the initial-boundary value problem for the forced nonlinear Schrödinger equation with a potential on the half-line is locally and (under stronger conditions) globally well posed, i.e. that there is a unique solution that depends continuously on the force at the boundary and on the initial data. We allow for a large class of unbounded potentials. Actually, for local s...
متن کاملRobin-to-robin Maps and Krein-type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz Domains
We study Robin-to-Robin maps, and Krein-type resolvent formulas for Schrödinger operators on bounded Lipschitz domains in R, n > 2, with generalized Robin boundary conditions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Proceedings. Mathematical, physical, and engineering sciences
دوره 469 2159 شماره
صفحات -
تاریخ انتشار 2013