A split-step Fourier method for the complex modified Korteweg-de Vries equation

Computers and Mathematics with Applications

Volumn 45, Issue 1-3, 2003, Pages 503-514

  Muslu, G M ^a   Erbay, H A ^a  

^a ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Fourier method; Nonlinear waves; Split step method; Two coupled MKdV equations

Indexed keywords

APPROXIMATION THEORY; FOURIER TRANSFORMS; PLASMA WAVES; PROBLEM SOLVING; RUNGE KUTTA METHODS; WAVE PROPAGATION;

COMPUTATIONAL COSTS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0037284595     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)80033-0     Document Type: Article

References (19)

1. C.F.F. Karney, A. Sen and F.Y.F. Chu, Nonlinear evolution of lower hybrid waves, Phys. Fluids 22, 940-952 (1979).
2. O.B. Gorbacheva and L.A. Ostrovsky, Nonlinear vector waves in a mechanical model of a molecular chain, Physica D 8, 223-228 (1983).
3. S. Erbay and E.S. Suhubi, Nonlinear wave propagation in micropolar media II. Special cases, solitary waves and Painlevé analysis, Int. J. Engng. Sci. 27, 915-919 (1989).
4. H.A. Erbay, Nonlinear transverse waves in a generalized elastic solid and the complex modified Korteweg-de Vries equation, Physica Scripta 58, 9-14 (1998).
5. F. Tappert, Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method, Lect. Appl. Math. Amer. Math. Soc. 15, 215 (1974).
6. T.R. Taha and M.J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation, J. Comput. Phys. 55, 203-230 (1984).
7. J.A.C. Weideman and B.M. Herbst, Split-step methods for the solution of the nonlinear Schrödinger equation, SIAM J. Numer. Anal. 23, 485-507 (1986).
8. D. Pathria and J.L. Morris, Pseudo-spectral solution of nonlinear Schrödinger equations, J. Comput. Phys. 87, 108-125 (1990).
9. B. Fornberg and T.A. Driscoll, A fast spectral algorithm for nonlinear wave equations with linear dispersion, J. Comput. Phys. 155, 456-467 (1999).
10. T.R. Taha and M.J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. IV, Numerical, Korteweg-de Vries equation, J. Comput. Phys. 55, 231-253 (1984).
11. T.R. Taha and M.J. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. IV. Numerical, modified Korteweg-de Vries equation, J. Comput. Phys. 77, 540-548 (1988).
12. B.M. Herbst, M.J. Ablowitz and E. Ryan, Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation, Computer Physics Communications 65, 137-142 (1991).
13. T.R. Taha, Numerical simulations of the complex modified Korteweg-de Vries equation, Mathematics and Computers in Simulation 37, 451-467 (1994).
14. J.M. Sanz-Serna and M.P. Calve, Numerical Hamiltonian Problems, Chapman and Hall, London, (1994).
15. H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A 150, 262-268 (1990).
16. M. Suzuki, General theory of higher-order decomposition of exponential operators and symplectic operators, Phys. Lett. A 165, 387-395 (1992).
17. R. McLachlan, Symplectic integration of Hamiltonian wave equation, Numer. Math. 66, 465-492 (1994).
18. J.A.C. Weideman and A. Cloet, Spectral methods and mappings for the evolution equations on the infinite line, Comp. Meth. App. Mech. Engng. 80, 467-481 (1990).
19. B. Fornberg and G.B. Whitham, A numerical and theoretical study of certain nonlinear wave phenomena, Phil. Trans. Roy. Soc. London A 289, 373-404 (1978).