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A multisymplectic variational integrator for the nonlinear Schrödinger equation
Author(s) -
Chen JingBo,
Qin MengZhao
Publication year - 2002
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10021
Subject(s) - variational integrator , integrator , mathematics , nonlinear system , variational principle , mathematical analysis , point (geometry) , schrödinger's cat , mathematical physics , physics , geometry , quantum mechanics , voltage
The multisymplectic structure for the nonlinear Schrödinger equation is presented. Based on the multisymplectic structure, we derive a nine‐point variational integrator from the discrete variational principle and a six‐point multisymplectic integrator from the Preissman multisymplectic scheme. We show that the two integrators are essentially equivalent. Therefore, we call it a multisymplectic variational integrator. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 523–536, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10021