Conservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG

P. E. Castillo, S. A. Gómez

Abstract


Conservation of the energy and the Hamiltonian of a general non linear Schr¨odinger equation is analyzed for the finite element method “Local Discontinuous Galerkin” spatial discretization. Conservation of the discrete analogue of these quantities is also proved for the fully discrete problem using the modified Crank-Nicolson method as time marching scheme. The theoretical results are validated on a series of problems
for different nonlinear potentials.

Keywords


Nonlinear Schr¨odinger equation; Local Discontinuous Galerkin method; energy and Hamiltonian conservation; modified Crank- Nicolson.

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Revista Mexicana de Física E

ISSN: 1870-3542

Semiannual publication of Sociedad Mexicana de Física, A.C.
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