A multisymplectic integrator for the periodic nonlinear Schrödinger equation

Applied Mathematics and Computation

Volumn 170, Issue 2, 2005, Pages 1394-1417

  Chen, Jing Bo ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Multisymplectic integrator; Nonlinear Schr dinger equation

Indexed keywords

DIFFERENTIAL EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; FINITE ELEMENT METHOD;

MULTISYMPLETIC INTEGRATOR; NONLINEAR SCHRÖDINGER EQUATION; NONLINEAR STABILITY;

NONLINEAR EQUATIONS;

EID: 27144436424     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.01.031     Document Type: Article

References (24)

1. M.J. Ablowitz, and J.F. Ladik A nonlinear difference scheme and inverse scattering Stud. Appl. Math 55 1976 213 229
2. S.C. Brenner, and L.R. Scott The mathematical theory of finite element methods 1994 Springer-Verlag New York
3. T.J. Bridges Multi-symplectic structures and wave propagation Math. Proc. Cam. Phil. Soc. 121 1997 147 190
4. T.J. Bridges, and S. Reich Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity Phys. Lett. A 284 2001 184 193
5. J.B. Chen Total variation in discrete multisymplectic field theory and multisymplectic energy momentum integrators Lett. Math. Phys. 61 2002 63 73
6. J.B. Chen, H.Y. Guo, and K. Wu Total variation in Hamiltonian formalism and symplectic-energy integrators J. Math. Phys. 44 2003 1688 1702
7. J.B. Chen, M.Z. Qin, and Y.F. Tang Symplectic and multisymplectic methods for the nonlinear Schrödinger equation Comput. Math. Appl. 43 2002 1095 1106
8. J.B. Chen A multisymplectic variational integrator for the nonlinear Schrödinger equation Numer. Meth. Part. Diff. Eq. 18 2002 523 536
9. J.B. Chen, Variational integrators for discrete multisymplectic field theory based on the finite element method, preprint.
10. P.G. Ciarlet Numerical analysis of the finite element method 1976 Les Presses de L'Université de Montreal, Quebec
11. P.G. Ciarlet The finite element method for elliptic problems 1978 North-Holland Amsterdam, New York, Oxford
12. M. Delfour, M. Fortin, and G. Payre Finite-difference solutions of a nonlinear Schrödinger equation J. Comput. Phys. 44 1981 277 288
13. P.L. Garcia The Poincaré-Cartan invariant in the calculus of variations Symp. Math. 14 1974 219 246
14. A. Hasegawa Optical solitons in fibers 1989 Springer-Verlag Berlin
15. B.M. Herbst, F. Varadi, and M.J. Ablowitz Symplectic methods for the nonlinear Schrödinger equation Math. Comput. Simul. 37 1994 353 369
16. J.L. Hong, Y. Liu, H. Munthe-Kass, A. Zanna, On a multisymplectic scheme for Schrödinger equations with variable coefficients, preprint.
17. G.L. Lamb Elements of soliton theory 1980 John Wiley & Sons New York
18. J.E. Marsden, G.W. Patrick, and S. Shkoller Multisymplectic geometry, variational integrators, and nonlinear PDEs Comm. Math. Phys. 199 1998 351 395
19. R. McLachlan Symplectic integration of Hamiltonian wave equations Numer. Math. 66 1994 465 492
20. P.J. Olver Applications of Lie groups to differential equations second ed. 1993 Springer-Verlag New York
21. S. Reich Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations J. Comput. Phys. 157 2000 473 499
22. C.M. Schober Symplectic integrators for Ablowitz-Ladik discrete nonlinear Schrödinger equation Phys. Lett. A 259 1999 140 151
23. Y.F. Tang, L. Vázquez, F. Zhang, and V.M. Pérez-García Symplectic methods for the nonlinear Schrödinger equation Comput. Math. Appl. 32 1996 73 83
24. S.B. Wineberg, J.F. McGrath, E.F. Gabl, L.R. Scott, and C.E. Southwell Implicit spectral methods for wave propagation problems J. Comput. Phys. 97 1991 311 336