scholarly journals Solving the nonlinear Schrödinger equation using energy conserving Hamiltonian boundary value methods

2017 ◽  
Author(s):  
L. Barletti ◽  
L. Brugnano ◽  
G. Frasca Caccia ◽  
F. Iavernaro
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Nonlinear Schrodinger Equation ◽  
Boundary Value Methods ◽  
Nonlinear Schrödinger ◽  
Hamiltonian Boundary Value Methods ◽  
Energy Conserving

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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