scholarly journals Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130341 ◽  
Author(s):  
Elena I. Kaikina
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Robin Boundary

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.

scholarly journals On an initial-boundary value problem for the nonlinear Schrödinger equation

1979 ◽  
Vol 2 (3) ◽  
pp. 503-522 ◽  
Author(s):  
Herbert Gajewski
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Initial Boundary Value

We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.

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