Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times
作者： Ludwig Gauckler , Christian Lubich
DOI: 10.1007/S10208-010-9063-3
关键词:
摘要: Conservation properties of a full discretization via spectral semi-discretization in space and Lie–Trotter splitting time for cubic Schrodinger equations with small initial data (or nonlinearity) are studied. The approximate conservation the actions linear equation, energy, momentum over long times is shown using modulated Fourier expansions. results valid arbitrary spatial dimension.
springer.com
sci-hub.se 参考文章(15)
Christian Lubich, Ernst Hairer, Gerhard Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations ,(2009)
Eric Paturel, Erwan Faou, Birkhoff normal form and splitting methods for semi linear Hamiltonian PDEs. Part II: Abstract splitting. arXiv: Numerical Analysis. ,(2008)
Eric Paturel, Erwan Faou, Benoit Grebert, Birkhoff normal form and splitting methods for semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization arXiv: Numerical Analysis. ,(2008)
L. Hakan Eliasson, Sergei Kuksin, KAM for the nonlinear Schrödinger equation Annals of Mathematics. ,vol. 172, pp. 371- 435 ,(2010) , 10.4007/ANNALS.2010.172.371
J. Bourgain, QUASI-PERIODIC SOLUTIONS OF HAMILTONIAN PERTURBATIONS OF 2D LINEAR SCHRODINGER EQUATIONS Annals of Mathematics. ,vol. 148, pp. 363- 439 ,(1998) , 10.2307/121001
David Cohen, Ernst Hairer, Christian Lubich, Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations Numerische Mathematik. ,vol. 110, pp. 113- 143 ,(2008) , 10.1007/S00211-008-0163-9
J. A. C. Weideman, B. M. Herbst, Split-step methods for the solution of the nonlinear Schro¨dinger equation SIAM Journal on Numerical Analysis. ,vol. 23, pp. 485- 507 ,(1986) , 10.1137/0723033
David Cohen, Ernst Hairer, Christian Lubich, Long-Time Analysis of Nonlinearly Perturbed Wave Equations Via Modulated Fourier Expansions Archive for Rational Mechanics and Analysis. ,vol. 187, pp. 341- 368 ,(2008) , 10.1007/S00205-007-0095-Z
D. Bambusi, B. Grébert, Birkhoff normal form for partial differential equations with tame modulus Duke Mathematical Journal. ,vol. 135, pp. 507- 567 ,(2006) , 10.1215/S0012-7094-06-13534-2
Erwan Faou, Benoît Grébert, Eric Paturel, Birkhoff normal form for splitting methods applied to semilinear Hamiltonian PDEs. Part I. Finite-dimensional discretization Numerische Mathematik. ,vol. 114, pp. 429- 458 ,(2009) , 10.1007/S00211-009-0258-Y