Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation

Mathematics and Computers in Simulation

Volumn 67, Issue 6, 2005, Pages 581-595

  Muslu, G M ^a   Erbay, H A ^a  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Fourier method; Generalized nonlinear Schr dinger equation; Solitary waves; Split step method

Indexed keywords

INTEGRAL EQUATIONS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DISPERSIVE WAVE EQUATIONS; FOURIER METHODS; SOLITARY WAVES;

NONLINEAR EQUATIONS;

EID: 10644227675     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2004.08.002     Document Type: Article

References (19)

1. J.P. Boyd, The rate of convergence of Fourier coefficients for entire functions of infinite order with application to the Weideman-Cloot sinh-mapping for pseudospectral computations on an infinite interval, J. Comput. Phys. 110 (1994) 360.
2. Q. Chang, E. Jia, W. Sun, Difference schemes for solving the generalized nonlinear Schrödinger equation, J. Comput. Phys. 148 (1999) 397.
3. A. Cloot, B.M. Herbst, J.A. Weideman, A numerical study of the nonlinear Schrödinger equation involving quintic terms, J. Comput. Phys. 86 (1990) 127.
4. B. Fornberg, T. A. Driscoll, A fast spectral algorithm for nonlinear wave equations with linear dispersion, J. Comput. Phys. 155(1999)456.
5. R.I. McLachlan, G.R.W. Quispel, Splitting methods, Acta Numer. 11 (2002) 341-434.
6. R. McLachlan, Symplectic integration of Hamiltonian wave equations, Numer. Math. 66 (1994) 465.
7. G.M. Muslu, H.A. Erbay, A split-step Fourier method for the complex modified Korteweg-de Vries equation, Comput. Math. Appl. 45 (2003) 503.
8. D. Pathria, J.LI. Morris, Exact solutions for a generalized nonlinear Schrodinger equation, Phys. Scripta 39 (1989) 673.
9. D. Pathria, J.LI. Morris, Pseudo-spectral solution of nonlinear Schrödinger equations, J. Comput. Phys. 87 (1990) 108.
10. M.P. Robinson, The solution of nonlinear Schrödinger equations using orthogonal spline collocation, Comput. Math. Appl. 33(1997)39.
11. B.F. Sanders, N.D. Katopodes, J.P. Boyd, Spectral modeling of nonlinear dispersive waves, J. Hydraulic Eng. 124 (1998) 1.
12. J.M Sanz-Serna, M.P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London, 1994.
13. Q. Sheng, A.Q.M. Khaliq, E.A. Al-Said, Solving the generalized nonlinear Schrödinger equation via quartic spline approximation, J. Comput. Phys. 166 (2001) 400.
14. M. Suzuki, General theory of higher-order decomposition of exponential operators and symplectic operators, Phys. Lett. A 165 (1992) 387.
15. T.R. Taha, M.J. Ablowitz, Analytical numerical aspects of certain nonlinear evolution equations. Part II. Numerical, non-linear Schrödinger equation, J. Comput. Phys. 55 (1984) 203.
16. F. Tappert, Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method, Lect. Appl. Math. Am. Math. Soc. 15 (1974) 215.
17. J.A.C. Weideman, B.M. Herbst, Split-step methods for the solution of the nonlinear Schrödinger equation, SIAM J. Num. Anal. 23 (1986) 485.
18. J.A.C. Weideman, A. Cloot, Spectral methods and mappings for the evolution equations on the infinite line, Comput. Meth. Appl. Mech. Eng. 80 (1990) 467.
19. H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A 150 (1990) 262.