메뉴 건너뛰기




Volumn 144, Issue 2-3, 2003, Pages 215-235

Numerical methods for the simulation of trapped nonlinear Schrödinger systems

Author keywords

Finite difference schemes; Nonlinear Schr dinger equations; Pseudospectral schemes; Symplectic schemes

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; NONLINEAR EQUATIONS;

EID: 0037774726     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00402-2     Document Type: Article
Times cited : (44)

References (38)
  • 7
    • 0043222983 scopus 로고    scopus 로고
    • Bose-Einstein solitons in highly asymmetric traps
    • Pérez-García V.M., Michinel H., Herrero H. Bose-Einstein solitons in highly asymmetric traps. Phys. Rev. A. 57:1998;3837-3845.
    • (1998) Phys. Rev. A , vol.57 , pp. 3837-3845
    • Pérez-García, V.M.1    Michinel, H.2    Herrero, H.3
  • 8
    • 39249085738 scopus 로고    scopus 로고
    • Dark-bright solitons in inhomogeneous Bose-Einstein condensates
    • Busch T., Anglin J.R. Dark-bright solitons in inhomogeneous Bose-Einstein condensates. Phys. Rev. Lett. 87:2001;010401:1-4.
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 0104011-0104014
    • Busch, T.1    Anglin, J.R.2
  • 9
    • 0000385916 scopus 로고    scopus 로고
    • Motion of dark solitons in trapped Bose-Einstein condensates
    • Busch T., Anglin J.R. Motion of dark solitons in trapped Bose-Einstein condensates. Phys. Rev. Lett. 84:2000;2298-2301.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2298-2301
    • Busch, T.1    Anglin, J.R.2
  • 12
    • 49149137309 scopus 로고
    • Finite difference solutions of a nonlinear Schrödinger equation
    • Delfour M., Fortin M., Payre G. Finite difference solutions of a nonlinear Schrödinger equation. J. Comp. Phys. 44:1981;277-288.
    • (1981) J. Comp. Phys. , vol.44 , pp. 277-288
    • Delfour, M.1    Fortin, M.2    Payre, G.3
  • 13
    • 77957214313 scopus 로고
    • Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation
    • Sanz-Serna J.M., Verwer J.G. Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation. IMA J. Numer. Anal. 6:1986;25-42.
    • (1986) IMA J. Numer. Anal. , vol.6 , pp. 25-42
    • Sanz-Serna, J.M.1    Verwer, J.G.2
  • 14
    • 0000722453 scopus 로고
    • A finite difference scheme for solving a nonlinear Schrödinger equation with a linear damping term
    • Peranich L.S. A finite difference scheme for solving a nonlinear Schrödinger equation with a linear damping term. J. Comp. Phys. 68:1987;501-505.
    • (1987) J. Comp. Phys. , vol.68 , pp. 501-505
    • Peranich, L.S.1
  • 15
    • 0010295721 scopus 로고
    • Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
    • Zhang F., Pérez-García V.M., Vázquez L. Numerical simulation of nonlinear Schrödinger systems: a new conservative scheme. Appl. Math. Comput. 71:1995;164-177.
    • (1995) Appl. Math. Comput. , vol.71 , pp. 164-177
    • Zhang, F.1    Pérez-García, V.M.2    Vázquez, L.3
  • 18
    • 0039756618 scopus 로고    scopus 로고
    • A space-time finite element method for the nonlinear Schrödinger equation: The discontinuous Galerkin method
    • Karakashian O., Makridakis C. A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method. Math. Comput. 67:1998;479-499.
    • (1998) Math. Comput. , vol.67 , pp. 479-499
    • Karakashian, O.1    Makridakis, C.2
  • 19
    • 38249029515 scopus 로고
    • An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schrödinger equation
    • Tourigny Y., Morris J. An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schrödinger equation. J. Comp. Phys. 76:1988;103-130.
    • (1988) J. Comp. Phys. , vol.76 , pp. 103-130
    • Tourigny, Y.1    Morris, J.2
  • 20
    • 0028766065 scopus 로고
    • Symplectic methods for the nonlinear Schrödinger equation
    • Herbst B.M., Varadi F., Ablowitz M.J. Symplectic methods for the nonlinear Schrödinger equation. Math. Comput. Simul. 37:1994;353-369.
    • (1994) Math. Comput. Simul. , vol.37 , pp. 353-369
    • Herbst, B.M.1    Varadi, F.2    Ablowitz, M.J.3
  • 21
    • 34249766017 scopus 로고
    • Symplectic integration of Hamiltonian wave equations
    • MacLahan R. Symplectic integration of Hamiltonian wave equations. Numer. Math. 66:1994;465-492.
    • (1994) Numer. Math. , vol.66 , pp. 465-492
    • MacLahan, R.1
  • 22
    • 0003172958 scopus 로고
    • Pseudo-spectral solution of nonlinear Schrödinger equations
    • Pathria D., Morris J.Ll. Pseudo-spectral solution of nonlinear Schrödinger equations. J. Comp. Phys. 87:1990;108-125.
    • (1990) J. Comp. Phys. , vol.87 , pp. 108-125
    • Pathria, D.1    Morris, J.Ll.2
  • 23
    • 0022738251 scopus 로고
    • Split-step methods for the solution of the nonlinear Schrödinger equation
    • Weideman J.A.C., Herbst B.M. Split-step methods for the solution of the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 23:1986;485-507.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 485-507
    • Weideman, J.A.C.1    Herbst, B.M.2
  • 24
    • 21844495492 scopus 로고
    • High-order split-step exponential methods for solving coupled nonlinear Schrödinger equations
    • Bandrauk A.D., Shen H. 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
  • 25
    • 0001257175 scopus 로고
    • Numerical experience with the nonlinear Schrödinger equation
    • Herbst B.M., Morris J.Ll., Mitchell A.R. Numerical experience with the nonlinear Schrödinger equation. J. Comput. Phys. 60:1985;282-305.
    • (1985) J. Comput. Phys. , vol.60 , pp. 282-305
    • Herbst, B.M.1    Morris, J.Ll.2    Mitchell, A.R.3
  • 26
    • 48549114390 scopus 로고
    • Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical nonlinear Schrödinger equation
    • Taha T.R., Ablowitz M.J. Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical nonlinear Schrödinger equation. J. Comp. Phys. 55:1984;203-230.
    • (1984) J. Comp. Phys. , vol.55 , pp. 203-230
    • Taha, T.R.1    Ablowitz, M.J.2
  • 29
    • 0004245694 scopus 로고
    • M. Abramowitz, & I.A. Stegun. New York: Dover
    • Abramowitz M., Stegun I.A. Handbook of Mathematical Functions. 1964;Dover, New York.
    • (1964) Handbook of Mathematical Functions
  • 30
    • 0012856949 scopus 로고
    • Uniqueness of positive radial solutions of Δu + f(|x|,u) = 0
    • Erbe L., Tang M. Uniqueness of positive radial solutions of. Δu+f(|x|,u)=0 Diff. Int. Eq. 11:1995;725-743.
    • (1995) Diff. Int. Eq. , vol.11 , pp. 725-743
    • Erbe, L.1    Tang, M.2
  • 31
    • 0033589578 scopus 로고    scopus 로고
    • Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
    • Wang Z.-Q. Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations. J. Diff. Eq. 159:1999;102-137.
    • (1999) J. Diff. Eq. , vol.159 , pp. 102-137
    • Wang, Z.-Q.1
  • 32
    • 0035509440 scopus 로고    scopus 로고
    • Construction of exact solutions by spatial translations in inhomogeneous nonlinear Schrödinger equations
    • García-Ripoll J.J., Pérez-García V.M., Vekslerchik V. Construction of exact solutions by spatial translations in inhomogeneous nonlinear Schrödinger equations. Phys. Rev. E. 64:2001;056602-1:6.
    • (2001) Phys. Rev. E , vol.64 , pp. 0566021-0566026
    • García-Ripoll, J.J.1    Pérez-García, V.M.2    Vekslerchik, V.3
  • 33
    • 0036344565 scopus 로고    scopus 로고
    • Minimization of Schrödinger functionals using sobolev gradients: Applications to quantum mechanics and nonlinear optics
    • García-Ripoll J.J., Pérez-García V.M. Minimization of Schrödinger functionals using sobolev gradients: Applications to quantum mechanics and nonlinear optics. SIAM J. Sci. Comp. 23:2001;1315-1324.
    • (2001) SIAM J. Sci. Comp. , vol.23 , pp. 1315-1324
    • García-Ripoll, J.J.1    Pérez-García, V.M.2
  • 34
    • 0030547910 scopus 로고    scopus 로고
    • Square-preserving and symplectic structure and scheme for quantum system
    • Ding P.Z., Wu C.X., Mu Y.K., Li Y.X., Jin M.X. Square-preserving and symplectic structure and scheme for quantum system. Chin. Phys. Lett. 13:1996;245-248.
    • (1996) Chin. Phys. Lett. , vol.13 , pp. 245-248
    • Ding, P.Z.1    Wu, C.X.2    Mu, Y.K.3    Li, Y.X.4    Jin, M.X.5
  • 35
    • 0032381616 scopus 로고    scopus 로고
    • Study of a symplectic scheme for the time evolution of an atom in an external field
    • Zhou Z.Y., Ding P.Z., Pan S.P. Study of a symplectic scheme for the time evolution of an atom in an external field. J. Kor. Phys. Soc. 32:1998;417-424.
    • (1998) J. Kor. Phys. Soc. , vol.32 , pp. 417-424
    • Zhou, Z.Y.1    Ding, P.Z.2    Pan, S.P.3
  • 36
    • 0034692187 scopus 로고    scopus 로고
    • Numerical solution of one-dimensional time-independent Schrödinger equation by using symplectic schemes
    • Liu X., Liu X., Zhou Z., Ding P., Pan S. Numerical solution of one-dimensional time-independent Schrödinger equation by using symplectic schemes. Int. J. Quant. Chem. 79:2000;343-349.
    • (2000) Int. J. Quant. Chem. , vol.79 , pp. 343-349
    • Liu, X.1    Liu, X.2    Zhou, Z.3    Ding, P.4    Pan, S.5
  • 37
    • 0000074154 scopus 로고    scopus 로고
    • Symplectic integrators tailored to the time-dependent Schrödinger equation
    • Gray S.K., Manolopoulos D.E. Symplectic integrators tailored to the time-dependent Schrödinger equation. J. Chem. Phys. 104:1996;7099-7112.
    • (1996) J. Chem. Phys. , vol.104 , pp. 7099-7112
    • Gray, S.K.1    Manolopoulos, D.E.2
  • 38
    • 0037095343 scopus 로고    scopus 로고
    • Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrom methods
    • Blanes S., Moan P.C. Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrom methods. J. Comput. Appl. Math. 142:2002;313-330.
    • (2002) J. Comput. Appl. Math. , vol.142 , pp. 313-330
    • Blanes, S.1    Moan, P.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.