메뉴 건너뛰기




Volumn 32, Issue 5, 1996, Pages 73-83

Symplectic methods for the nonlinear Schrödinger equation

Author keywords

Formal energy; Invariants; Nonlinear Schr dinger equation; Symplectic methods

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NUMERICAL METHODS; QUANTUM THEORY;

EID: 0030241340     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(96)00136-8     Document Type: Article
Times cited : (78)

References (28)
  • 5
    • 49149137309 scopus 로고
    • Finite-difference solutions of a non-linear Schrödinger equation
    • M. Delfour, M. Fortin and G. Payre, Finite-difference solutions of a non-linear Schrödinger equation, J. Comp. Phys. 44 (2), 277-288 (1981).
    • (1981) J. Comp. Phys. , vol.44 , Issue.2 , pp. 277-288
    • Delfour, M.1    Fortin, M.2    Payre, G.3
  • 6
    • 48549114390 scopus 로고
    • Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
    • T.R. Taha and M. Ablowitz, Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation, J. Comp. Phys. 55 (2), 203-230 (1984).
    • (1984) J. Comp. Phys. , vol.55 , Issue.2 , pp. 203-230
    • Taha, T.R.1    Ablowitz, M.2
  • 7
    • 84961470712 scopus 로고
    • Methods for the numerical solution of the nonlinear Schrödinger equation
    • J.M. Sanz-Serna, Methods for the numerical solution of the nonlinear Schrödinger equation, Math. Comput. 43 (167/168), 21-27 (1984).
    • (1984) Math. Comput. , vol.43 , Issue.167-168 , pp. 21-27
    • Sanz-Serna, J.M.1
  • 8
    • 0001257175 scopus 로고
    • Numerical solution of the nonlinear Schrödinger equation
    • B.M. Herbst, J.Ll. Morris and A.R. Mitchell, Numerical solution of the nonlinear Schrödinger equation, J. Comp. Phys. 60 (2), 282-305 (1985).
    • (1985) J. Comp. Phys. , vol.60 , Issue.2 , pp. 282-305
    • Herbst, B.M.1    Morris, J.L.2    Mitchell, A.R.3
  • 9
    • 2442538708 scopus 로고
    • The convergence of numerical method for nonlinear Schrödinger equation
    • B.Y. Guo, The convergence of numerical method for nonlinear Schrödinger equation, J. Comp. Math. 4 (2), 121-130 (1986).
    • (1986) J. Comp. Math. , vol.4 , Issue.2 , pp. 121-130
    • Guo, B.Y.1
  • 10
    • 77957214313 scopus 로고
    • Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation
    • J.M. Sanz-Serna and J.G. Verwer, Conservative and nonconservative schemes for the solution of the nonlinear Schrödinger equation, IMA J. Numer. Anal. 6 (1), 25-42 (1986).
    • (1986) IMA J. Numer. Anal. , vol.6 , Issue.1 , pp. 25-42
    • Sanz-Serna, J.M.1    Verwer, J.G.2
  • 11
    • 38249029515 scopus 로고
    • An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schrödinger equation
    • Y. Tourigny and J. Morris, An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schrödinger equation, J. Comp. Phys. 76 (1), 103-130 (1988).
    • (1988) J. Comp. Phys. , vol.76 , Issue.1 , pp. 103-130
    • Tourigny, Y.1    Morris, J.2
  • 12
    • 0010295721 scopus 로고
    • Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
    • F. Zhang, V.M. Pérez-García and L. Vázquez, Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme, Appl. Math. Comput. 71 (2/3), 165-177 (1995).
    • (1995) Appl. Math. Comput. , vol.71 , Issue.2-3 , pp. 165-177
    • Zhang, F.1    Pérez-García, V.M.2    Vázquez, L.3
  • 13
    • 33746314863 scopus 로고
    • Symplectic integration of Hamiltonian systems
    • P.J. Channel and J.C. Scovel, Symplectic integration of Hamiltonian systems, Nonlinearity 3 (2), 231-259 (1990).
    • (1990) Nonlinearity , vol.3 , Issue.2 , pp. 231-259
    • Channel, P.J.1    Scovel, J.C.2
  • 15
    • 0002961720 scopus 로고
    • Construction of canonical difference schemes for Hamiltonian formalism via generating functions
    • K. Feng, H.M. Wu, M.Z. Qin and D.L. Wang, Construction of canonical difference schemes for Hamiltonian formalism via generating functions, J. Comput. Math. 7 (1), 71-96 (1989).
    • (1989) J. Comput. Math. , vol.7 , Issue.1 , pp. 71-96
    • Feng, K.1    Wu, H.M.2    Qin, M.Z.3    Wang, D.L.4
  • 16
    • 0003191706 scopus 로고
    • On the approximation of linear Hamiltonian-systems
    • Z. Ge and K. Feng, On the approximation of linear Hamiltonian-systems, J. Comput. Math. 6 (1), 88-97 (1988).
    • (1988) J. Comput. Math. , vol.6 , Issue.1 , pp. 88-97
    • Ge, Z.1    Feng, K.2
  • 17
    • 45449123467 scopus 로고
    • Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
    • Z. Ge and J.E. Marsden, Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators, Physics Letters A 133 (3), 134-139 (1988).
    • (1988) Physics Letters A , vol.133 , Issue.3 , pp. 134-139
    • Ge, Z.1    Marsden, J.E.2
  • 18
    • 0011615763 scopus 로고
    • Canonical Runge-Kutta methods
    • F.M. Lasagni, Canonical Runge-Kutta methods, ZAMP 39 (6), 952-953 (1988).
    • (1988) ZAMP , vol.39 , Issue.6 , pp. 952-953
    • Lasagni, F.M.1
  • 19
    • 0021428479 scopus 로고
    • Some properties of the discrete Hamiltonian method
    • C.R. Menyuk, Some properties of the discrete Hamiltonian method, Physica D 11 (1-3), 109-129 (1984).
    • (1984) Physica D , vol.11 , Issue.1-3 , pp. 109-129
    • Menyuk, C.R.1
  • 20
    • 0020798563 scopus 로고
    • A canonical integration technique
    • R.D. Ruth, A canonical integration technique, IEEE Trans. Nucl. Sci. 30 (4), 2669-2671 (1983).
    • (1983) IEEE Trans. Nucl. Sci. , vol.30 , Issue.4 , pp. 2669-2671
    • Ruth, R.D.1
  • 21
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian-systems
    • J.M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian-systems, BIT 28 (4), 877-883 (1988).
    • (1988) BIT , vol.28 , Issue.4 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 23
    • 0006355099 scopus 로고
    • Symplectic numerical integration of Hamiltonian systems
    • MSRI Series, (Edited by T. Ratiu), Springer-Verlag, New York
    • J.C. Scovel, Symplectic numerical integration of Hamiltonian systems, In The Geometry of Hamiltonian Systems, MSRI Series, Volume 22, (Edited by T. Ratiu), pp. 463-496, Springer-Verlag, New York, (1991).
    • (1991) The Geometry of Hamiltonian Systems , vol.22 , pp. 463-496
    • Scovel, J.C.1
  • 24
    • 0042475779 scopus 로고
    • On the preservation of the symplectic structure for numerical integration of Hamiltonian systems
    • Edited by S.S. Filippov, USSR Academy of Sciences, Moscow
    • Y.B. Suris, On the preservation of the symplectic structure for numerical integration of Hamiltonian systems, In Numerical Solution of Differential Equations, (Edited by S.S. Filippov), pp. 148-160, USSR Academy of Sciences, Moscow, (1988).
    • (1988) Numerical Solution of Differential Equations , pp. 148-160
    • Suris, Y.B.1
  • 25
    • 43949152659 scopus 로고
    • Formal energy of symplectic scheme for Hamiltonian systems and its applications (I)
    • Y.F. Tang, Formal energy of symplectic scheme for Hamiltonian systems and its applications (I), Computers Math. Applic. 27 (7), 31-39 (1994).
    • (1994) Computers Math. Applic. , vol.27 , Issue.7 , pp. 31-39
    • Tang, Y.F.1
  • 26
    • 0001005075 scopus 로고
    • Construction of higher-order symplectic integrators
    • H. Yoshida, Construction of higher-order symplectic integrators, Physics Letters A 150 (5-7), 262-268 (1990).
    • (1990) Physics Letters A , vol.150 , Issue.5-7 , pp. 262-268
    • Yoshida, H.1
  • 28
    • 0000471386 scopus 로고
    • An envelope soliton problem
    • J.W. Miles, An envelope soliton problem, SIAM J. Appl. Math. 41 (2), 227-230 (1981).
    • (1981) SIAM J. Appl. Math. , vol.41 , Issue.2 , pp. 227-230
    • Miles, J.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.