Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations

Applied Mathematics and Computation

Volumn 179, Issue 2, 2006, Pages 596-605

  Xu, Zhenli ^a   He, Jingsong ^a   Han, Houde ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Higher order nonlinear Schr dinger equation; Operator splitting Pad method; Optical solitons

Indexed keywords

COMPUTATION THEORY; FINITE DIFFERENCE METHOD; OPTICAL FIBERS; SOLITONS; WAVE PROPAGATION;

COLLISION BEHAVIORS; HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION; OPERATOR SPLITTING PADÉ METHOD (OSPD); OPTICAL SOLITONS;

NONLINEAR EQUATIONS;

EID: 33748077411     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.12.001     Document Type: Article

References (19)

1. Hasegawa A. Optical Solitons in Fibers (1989), Springer, Heidelberg
2. Porsezian K., and Nakkeeran K. Optical solitons in presence of Kerr dispersion and self-frequency shift. Phys. Rev. Lett. 76 (1996) 3955-3958
3. Agrawal G.P. Nonlinear Fiber Optics (2001), Academic Press, San Diego
4. Pathria D., and Morris J.L. Pseudo-spectral solution of nonlinear Schrödinger equations. J. Comput. Phys. 87 (1990) 108-125
5. Chen J.B., Qin M.Z., and Tang Y.F. Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation. Comp. Math. Appl. 43 (2002) 1095-1106
6. Gardner L., Gardner G., Zaki S., and Sahrawi Z.E. B-spline finite element studies of the non-linear Schrödinger equation. Comput. Methods Appl. Mech. Eng. 108 (1993) 303-318
7. Taha T.R., and Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations, II: numerical, nonlinear Schrödinger equation. J. Comput. Phys. 55 (1984) 203-230
8. Chang Q.S., Jia E.H., and Sun W. Difference schemes for solving the generalized nonlinear Schrödinger equation. J. Comp. Phys. 148 (1999) 397-415
9. McLachlan R.I., and Quispel G.R.W. Splitting methods. Acta Numer. 11 (2002) 341-434
10. Yoshida H. Construction of higher order symplectic integrators. Phys. Lett. A 150 (1990) 262-268
11. Holden H., Karlsen K.H., and Risebroz N.H. Operator splitting methods for generalized Korteweg-de Vries equations. J. Comp. Phys. 153 (1999) 203-222
12. Bao W.Z., Jin S., and Markowich P.A. On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. J. Comp. Phys. 175 (2002) 487-524
13. Bao W.Z., Jin S., and Markowich P.A. Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semi-classical regimes. SIAM J. Sci. Comp. 25 (2003) 27-64
14. Blow K.J. System analysis using the split operator method. Lecture Notes in Physics vol. 613 (2003), Springer, Heidelberg 127-140
15. Wang H.Q. Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations. Appl. Math. Comput. 170 (2005) 17-35
16. Lele S.K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16-42
17. M.W. Reinsch, A simple expression for the terms in the Baker-Campbell-Hausdorff series, preprint, 13 January 2000. http://arxiv.org/abs/math-ph/9905012/.
18. Sanders B.F., Katopodes N.D., and Boyd J.P. Spectral modeling of nonlinear dispersive waves. J. Hydraul. Eng. 124 (1998) 2-12
19. Muslu G.M., and Erbay H.A. Higher-order split-step Fourier schemes for the generalized Schrödinger equation. Math. Comput. Simul. 67 (2005) 581-595