A novel numerical approach to simulating nonlinear Schrödinger equations with varying coefficients

Applied Mathematics Letters

Volumn 16, Issue 5, 2003, Pages 759-765

  Hong, Jialin ^a   Liu, Ying ^b  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Multisymplecticity; Nonlinear Schr dinger equation; Quasi periodic solitary waves

Indexed keywords

EID: 84867955067     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(03)00079-X     Document Type: Article

References (18)

1. M.J Ablowitz, and P.A Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering 1991 Cambridge University Press Cambridge, England
2. G.P Agrawal Nonlinear Fiber Optics 1995 Academic New York
3. N Akhmediev, and A Ankiewicz Solitons, Nonlinear Pulses and Beams 1997 Chapman Hall London
4. A Hasegawa, and Y Kodama Solitons in Optical Communications 1995 Oxford University Press Oxford
5. J Hong, and Y Liu Multi-symplecticity of the centered box discretizations for a class of Hamiltonian PDEs and an application to quasi-periodically solitary wave of gpKdV equation 2001 Preprint
6. V.N Serkin, and A Hasegawa Novel soliton solutions of the nonlinear Schrödinger equation model Phys. Rev. Lett. 85 2000 4502
7. T.J Bridges, and S Reich Multi-symplectic integrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity 1999 Preprint
8. J Chen New schemes for the nonlinear Schrödinger equation Appl. Math. Comput. 124 2001 371 379
9. J Chen, and M.-Z Qin Multisymplectic geometry and multisymplectic integrators for the nonlinear Schrödinger equation 2000 Preprint
10. J Hong, and M.-Z Qin Multi-symplecticity of the centered box discretizations for Hamiltonian PDEs with m-2 space dimensions Appl. Math. Lett. 15 8 2002 1005 1011
11. J. Hong and H. Munthe-Kaas, in preparation.
12. J.E Marsden, G.P Patrick, and S Shkoller Multisymplectic geometry, variational integrators, and nonlinear PDEs Comm. in Math. Phys. 199 1999 351 395
13. J.E Marsden, S Pekarsky, S Shkoller, and M West Variational methods, multisymplectic geometry and continuum mechanics J. Geom. and Phys. 38 2001 253 284
14. J.E Marsden, and S Shkoller Multisymplectic geometry, covariant Hamiltonians and water waves Math. Proc. Comb. Phil. Soc. 125 1999 553 575
15. S Reich Multi-symplectic Runge-Kutta methods for Hamiltonian wave equations J. Comput. Phy. 157 2000 473 499
16. J Hong, and Y Liu Numerical simulation of periodic and quasiperiodic solutions for nonautonomous Hamiltonian system via the scheme preserving weak invariance Comput. Phys. Commun. 131 1/2 2000 86 94
17. J Hong, and Y Liu Symplectic integrations of linear discontinuous Hamiltonian systems and an application to the numerical simulation of bounded solutions Neural, Parallel and Scientific Computations 8 200 317 326
18. F Zhang, V.M Perez-Garcia, and L Vazquez Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme Appl. Math. Comput. 71 199 165 177