메뉴 건너뛰기




Volumn 170, Issue 1, 2005, Pages 17-35

Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations

Author keywords

Bose Einstein Condensation; Gross Pitaevskii equation; Nonlinear Schr dinger equations; Split step finite difference method; Split step Fourier spectral method

Indexed keywords

FOURIER TRANSFORMS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

EID: 26844436587     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.10.066     Document Type: Article
Times cited : (165)

References (22)
  • 1
    • 0038045487 scopus 로고    scopus 로고
    • Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods
    • P. Muruganandam, and S.K Adhikari Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods J. Phys. B 36 2003 2501 2513
    • (2003) J. Phys. B , vol.36 , pp. 2501-2513
    • Muruganandam, P.1    Adhikari, S.K.2
  • 2
    • 0037408314 scopus 로고    scopus 로고
    • Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation
    • W. Bao, D. Jaksch, and P.A. Markowich Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation J. Comput. Phys. 187 1 2003 318 342
    • (2003) J. Comput. Phys. , vol.187 , Issue.1 , pp. 318-342
    • Bao, W.1    Jaksch, D.2    Markowich, P.A.3
  • 4
    • 36449006563 scopus 로고
    • Exponential split operator methods for solving coupled time-dependent Schrödinger equations
    • A.D. Bandrauk, and H. Shen Exponential split operator methods for solving coupled time-dependent Schrödinger equations J. Chem. Phys. 99 2 1993 1185 1193
    • (1993) J. Chem. Phys. , vol.99 , Issue.2 , pp. 1185-1193
    • Bandrauk, A.D.1    Shen, H.2
  • 5
    • 21844495492 scopus 로고
    • High-order split-step exponential methods for solving coupled nonlinear Schrödinger equations
    • A.D. Bandrauk, and H. Shen High-order split-step exponential methods for solving coupled nonlinear Schrödinger equations J. Phys. A-Math. Gen. 27 1994 7147 7155
    • (1994) J. Phys. A-Math. Gen. , vol.27 , pp. 7147-7155
    • Bandrauk, A.D.1    Shen, H.2
  • 6
    • 0034229732 scopus 로고    scopus 로고
    • Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: An application to trapped Bose-Einstein condensates
    • M.M. Cerimele, M.L. Chiofalo, F. Pistella, S. Succi, and M.P. Tosi Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: an application to trapped Bose-Einstein condensates Phys. Rev. E 62 2000 1382 1389
    • (2000) Phys. Rev. e , vol.62 , pp. 1382-1389
    • Cerimele, M.M.1    Chiofalo, M.L.2    Pistella, F.3    Succi, S.4    Tosi, M.P.5
  • 7
    • 0001160015 scopus 로고    scopus 로고
    • Difference schemes for solving the generalized nonlinear Schrödinger equation
    • Q. Chang, E. Jia, and W. Sun Difference schemes for solving the generalized nonlinear Schrödinger equation J. Comput. Phys. 148 1999 397 415
    • (1999) J. Comput. Phys. , vol.148 , pp. 397-415
    • Chang, Q.1    Jia, E.2    Sun, W.3
  • 8
    • 0038202144 scopus 로고    scopus 로고
    • Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
    • C.M. Dion, and E. Cances Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap Phys. Rev. E 67 2003 046706-1 046706-9
    • (2003) Phys. Rev. e , vol.67
    • Dion, C.M.1    Cances, E.2
  • 9
    • 0035858542 scopus 로고    scopus 로고
    • Stability of exact solutions of the defocusing nonlinear Schrödinger equation with periodic potential in two dimensions
    • B. Deconinck, B.A. Frigyik, and J.N. Kutz Stability of exact solutions of the defocusing nonlinear Schrödinger equation with periodic potential in two dimensions Phys. Lett. A 283 2001 177 184
    • (2001) Phys. Lett. A , vol.283 , pp. 177-184
    • Deconinck, B.1    Frigyik, B.A.2    Kutz, J.N.3
  • 10
    • 0041846755 scopus 로고    scopus 로고
    • Dynamics and stability of Bose-Einstein condensates: The nonlinear Schrödinger equation with periodic potential
    • B. Deconinck, B.A. Frigyik, and J.N. Kutz Dynamics and stability of Bose-Einstein condensates: the nonlinear Schrödinger equation with periodic potential J. Nonlinear Sci. 12 2002 169 205
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 169-205
    • Deconinck, B.1    Frigyik, B.A.2    Kutz, J.N.3
  • 11
    • 26844495568 scopus 로고    scopus 로고
    • Numerical methods for Schrodinger-type problems
    • A.H. Siddiqi M. Koevara Kluwer Academic Publishers Netherlands
    • G. Fairweather, and M. Khebchareon Numerical methods for Schrodinger-type problems A.H. Siddiqi M. Koevara Trends in Industrial and Applied Mathematics 2002 Kluwer Academic Publishers Netherlands 219 250
    • (2002) Trends in Industrial and Applied Mathematics , pp. 219-250
    • Fairweather, G.1    Khebchareon, M.2
  • 13
    • 0034920816 scopus 로고    scopus 로고
    • Taha numerical simulation of coupled nonlinear Schrödinger equation
    • M.S. Ismail, and R. Thiab Taha numerical simulation of coupled nonlinear Schrödinger equation Math. Comput. Simul. 56 2001 547 562
    • (2001) Math. Comput. Simul. , vol.56 , pp. 547-562
    • Ismail, M.S.1    Thiab, R.2
  • 14
    • 17144440094 scopus 로고    scopus 로고
    • Structure of vortex lattices in rotating two-component Bose-Einstein condensates
    • K. Kasamatsu, M. Tsubota, and M. Ueda Structure of vortex lattices in rotating two-component Bose-Einstein condensates Physica B 329-333 2003 23 24
    • (2003) Physica B , vol.329-333 , pp. 23-24
    • Kasamatsu, K.1    Tsubota, M.2    Ueda, M.3
  • 17
    • 0037774726 scopus 로고    scopus 로고
    • Numerical methods for the simulation of trapped nonlinear Schrödinger systems
    • V.M. Perez-Garcia, and X.Y. Liu Numerical methods for the simulation of trapped nonlinear Schrödinger systems Appl. Math. Comput. 144 2-3 2003 215 235
    • (2003) Appl. Math. Comput. , vol.144 , Issue.2-3 , pp. 215-235
    • Perez-Garcia, V.M.1    Liu, X.Y.2
  • 18
    • 84990553244 scopus 로고
    • Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation
    • P.L. Sulem, C. Sulem, and A. Patera Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation Commun. Pure Appl. Math. 37 1984 755 778
    • (1984) Commun. Pure Appl. Math. , vol.37 , pp. 755-778
    • Sulem, P.L.1    Sulem, C.2    Patera, A.3
  • 20
    • 0010289639 scopus 로고
    • A numerical scheme for the nonlinear Schrödinger equation
    • T.R. Taha A numerical scheme for the nonlinear Schrödinger equation Comput. Math. Appl. 22 9 1991 77 84
    • (1991) Comput. Math. Appl. , vol.22 , Issue.9 , pp. 77-84
    • Taha, T.R.1
  • 21
    • 0022738251 scopus 로고
    • Split-step methods for the solution of the nonlinear Schrödinger equation
    • J.A.C. Weideman, and B.M. Herbst Split-step methods for the solution of the nonlinear Schrödinger equation SIAM J. Numer. Anal. 23 3 1986 485 507
    • (1986) SIAM J. Numer. Anal. , vol.23 , Issue.3 , pp. 485-507
    • Weideman, J.A.C.1    Herbst, B.M.2
  • 22
    • 0001005075 scopus 로고
    • Construction of higher order symplectic integrators
    • H. Yoshida Construction of higher order symplectic integrators Phys. Lett. A 150 12 1990 262 268
    • (1990) Phys. Lett. A , vol.150 , Issue.12 , pp. 262-268
    • Yoshida, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.