Finite difference methods for an AKNS eigenproblem

Mathematics and Computers in Simulation

Volumn 43, Issue 1, 1997, Pages 77-88

  Weideman, J A C ^a   Herbst, B M ^b  

^a OREGON STATE UNIVERSITY   (United States)

^b UNIVERSITY OF THE FREE STATE   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DIFFERENCE EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

ABLOWITZ-LADIK SCHEME; AKNS EIGENPROBLEM; DISCRETIZATION; INVERSE SCATTERING METHOD; NONLINEAR SCHRODINGER EQUATION;

FINITE DIFFERENCE METHOD;

EID: 0030834016     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(96)00057-2     Document Type: Article

References (11)

1. M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, Cambridge, 1992.)
2. M.J. Ablowitz and B.M. Herbst, On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation, SIAM J. Appl. Math. 50 (1990) 339-351.
3. M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, The inverse-scattering transform-Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974) 249-315.
4. M.J. Ablowitz and J.F. Ladik, Nonlinear differential-difference equations and Fourier analysis, J. Math. Phys. 17 (1976) 1011-1018.
5. M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, PA, USA, 1981).
6. G. Boffetta and A.R. Osborne, Computation of the direct scattering transform for the nonlinear Schrödinger equation, J. Comput. Phys. 102 (1992) 252-263.
7. Y.C. Ma and M.J. Ablowitz, The periodic cubic Schrödinger equation, Stud.Appl. Math. 65 (1981) 113-158.
8. D.W. McLaughlin and C.M. Schober, Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation, Physica D 57 (1992) 447-465.
9. A.R. Osborne, The hyperelliptic inverse scattering transform for the periodic, defocusing nonlinear Schrödinger equation, J. Comput. Phys. 109 (1993) 93-107.
10. E.A. Overman II, D.W. McLaughlin and A.R. Bishop, Coherence and chaos in the driven-damped sine-Gordon equation: Measurement of the soliton spectrum, Physica D 19 (1986) 1-41.
11. J.D. Pryce, Numerical Solution of Sturm-Liouville Problems (Clarendon Press, Oxford, 1993.)