Local absorbing boundary conditions for two‐dimensional nonlinear Schrödinger equation with wave operator on unbounded domain

2021 ◽  
Author(s):  
Hongwei Li
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Unbounded Domain ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Absorbing Boundary Conditions ◽  
Two Dimensional ◽  
Absorbing Boundary

scholarly journals ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250026 ◽  
Author(s):  
XAVIER ANTOINE ◽  
CHRISTOPHE BESSE ◽  
PAULINE KLEIN
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
A Priori Estimates ◽  
Pseudodifferential Operators ◽  
A Priori ◽  
Absorbing Boundary Conditions ◽  
Two Dimensional ◽  
Absorbing Boundary ◽  
Priori Estimates

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.

Sign in / Sign up

Export Citation Format

Share Document