Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method

Mathematics and Computers in Simulation

Volumn 78, Issue 4, 2008, Pages 532-547

  Ismail, M S ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Coupled nonlinear Schr dinger equation; Galerkin method; Soliton interaction

Indexed keywords

BIREFRINGENCE; FINITE ELEMENT METHOD; GALERKIN METHODS; OPTICAL FIBERS; PROBLEM SOLVING; SCHRODINGER EQUATION;

LINEAR BIREFRINGENCE; NUMERICAL SOLUTION; SOLITON INTERACTION;

NONLINEAR EQUATIONS;

EID: 44349188784     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2007.07.003     Document Type: Article

References (24)

1. A. Aydin, B. Karasozen, Multi-symplectic integration of coupled nonlinear Schrödinger system with soliton solutions, Int. J. Comput. Math., in press.
2. A. Aydin, B. Karasozen, Symplectic and multisymplectic methods for the coupled nonlinear Schrödinger equations with periodic solutions, Comput. Phys. Commun. 177 (7) (2007) 566-583.
3. J. de Frutos, J.M. Sanz-Serna, An easily implementable fourth order method for the time integration of waves problems, Report 1991/2, Universidad De Valladolid, Spain, 1991.
4. D.F. Griffiths, A.R. Mitchell, J. Li Morris, A numerical study of the nonlinear Schrödinger equation, NA/52, University of Dundee, 1982.
5. Ismail M.S., and Taha T.R. A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation. Math. Comp. Simul. 74 (2007) 302-311
6. Ismail M.S., and Alamri S.Z. 'Highly accurate finite difference method for coupled nonlinear Schrödinger equation. Int. J. Comput. Math. 81 3 (2004) 333-351
7. Ismail M.S., and Taha T.R. Numerical simulation of coupled nonlinear Schrödinger equation. Math. Comput. Simul. 56 (2001) 547-562
8. Ismail M.S., and Taha T. A finite element solution for the coupled Schrödinger equation. Proceedings of the 16th IMACS World Congress on Scientific Computation. Lausanne (2000)
9. Ismail M.S. Finite difference method with cubic spline for solving nonlinear Schrödinger equation. Int. J. Comput. Math. 62 (1996) 101-112
10. Menyuk C.R. Stability of solitons in birefringent optical fibers. J. Opt. Soc. Am. B 5 (1998) 392-402
11. Muslu G.M., and Erbay H.A. Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation. Math. Comput. Simul. 67 (2005) 581-595
12. Sanz-Serna J.M., and Verwer J.G. Conservative and nonconservative Schrödinger equation. IMA J. Numer. Anal. 6 (1986) 25-42
13. Shamerdan A.B. The numerical treatment of the nonlinear Schrödinger equation. Comput. Math. Appl. 19 (1990) 67-73
14. Sheng Q., Khaliq A.Q.M., and Al-Said E.A. Solving the generalized nonlinear Schrödinger equation via quartic spline approximation. J. Comput. Phys. 166 (2001) 400-417
15. Somnnier W.J., and Christov C.I. Strong coupling of Schrödinger equations conservative scheme approach. Math. Comput. Simul. 69 (2005) 314-325
16. N.H. Sweilam, R.F. Al-Bar, Variational iteration method for coupled nonlinear Schrödinger equations, Comput. Math. Appl., in press.
17. Sun J.Q., Gu X.Y., and Ma Z.Q. Numerical study of the soliton waves of the coupled nonlinear Schrödinger system. Physica D 196 (2004) 311-328
18. Sun J.Q., and Qin M.Z. Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system. Comput. Phys. Commun. 155 (2003) 221-235
19. Wadati M., Izuka T., and Hisakado M. A coupled nonlinear Schrödirnger equation and optical solitons. J. Phys. Soc. Jpn. 61 7 (1992) 2241-2245
20. Wang H. Numerical studies on the split step finite difference method for the nonlinear Schrödinger equations. Appl. Math. Comput. 170 (2005) 17-35
21. A.M. Wazwaz, The variational method for rational solutions for KdV, K(2,2), Burger, and Cubic Boussinesq equation, J. Comput. Appl. Math. 207 (2007) 18-23.
22. A.M. Wazwaz, A study on linear and nonlinear Schrödinger equations by the variational iteration method, Chaos, Solitons & Fractals, in press.
23. Xu Y., and Shu C. Local discontinuous Galerkin method for nonlinear Schrödinger equations. J. Comput. Phys. 205 (2005) 72-97
24. Yang J. Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics. Phys. Rev. E 59 2 (1999) 2393-2405