Open AccessConservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG
Author(s) -
Paul Castillo,
Sergio Gómez
Publication year - 2018
Publication title -
revista mexicana de física e
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.178
H-Index - 10
eISSN - 2683-2216
pISSN - 1870-3542
DOI - 10.31349/revmexfise.64.52
Subject(s) - discretization , mathematics , hamiltonian (control theory) , mathematical physics , nonlinear system , conservation law , discontinuous galerkin method , mathematical analysis , finite element method , physics , mathematical optimization , quantum mechanics , thermodynamics
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 problemsfor different nonlinear potentials.