메뉴 건너뛰기




Volumn 226, Issue 2, 2007, Pages 1968-1984

Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients

Author keywords

Charge conservation law; Multi symplectic conservation law; Nonlinear Schr dinger equations; Runge Kutta Nystr m methods

Indexed keywords

NONLINEAR EQUATIONS; NUMERICAL METHODS; PHYSICAL PROPERTIES; SOLITONS;

EID: 34548697286     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.06.023     Document Type: Article
Times cited : (38)

References (23)
  • 1
    • 28844475048 scopus 로고    scopus 로고
    • On symplectic and multisymplectic schemes for the KdV equation
    • Ascher U.M., and McLachlan R.I. On symplectic and multisymplectic schemes for the KdV equation. J. Sci. Comput. 25 (2005) 83-104
    • (2005) J. Sci. Comput. , vol.25 , pp. 83-104
    • Ascher, U.M.1    McLachlan, R.I.2
  • 2
    • 0042137401 scopus 로고    scopus 로고
    • Muti-symplectic structures and wave propagation
    • Bridges T.J. Muti-symplectic structures and wave propagation. Math. Proc. Camb. Phil. Soc. 121 (1997) 147-190
    • (1997) Math. Proc. Camb. Phil. Soc. , vol.121 , pp. 147-190
    • Bridges, T.J.1
  • 3
    • 0037832748 scopus 로고    scopus 로고
    • Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve sysmplecticity
    • Bridges T.J., and Reich S. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve sysmplecticity. Phys. Lett. A 284 (2001) 184-193
    • (2001) Phys. Lett. A , vol.284 , pp. 184-193
    • Bridges, T.J.1    Reich, S.2
  • 4
    • 33645522650 scopus 로고    scopus 로고
    • Conserved quantities of some Hamiltonian wave equations after full discretization
    • Cano B. Conserved quantities of some Hamiltonian wave equations after full discretization. Numer. Math. 103 (2006) 197-223
    • (2006) Numer. Math. , vol.103 , pp. 197-223
    • Cano, B.1
  • 5
    • 0001160015 scopus 로고    scopus 로고
    • Difference schemes for solving the generalized nonlinear Schrödinger equation
    • Chang Q., Jia E., and Sun W. 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
  • 7
    • 84867955067 scopus 로고    scopus 로고
    • A novel numerical approach to simulating nonlinear Schrödinger equation with varying coefficients
    • Hong J., and Liu Y. A novel numerical approach to simulating nonlinear Schrödinger equation with varying coefficients. Appl. Math. Lett. 16 (2003) 759-765
    • (2003) Appl. Math. Lett. , vol.16 , pp. 759-765
    • Hong, J.1    Liu, Y.2
  • 8
    • 3543095217 scopus 로고    scopus 로고
    • Multi-symplecticity of the centred box discretization for a class of Hamiltonian PDEs and an application to quasi-periodically solitary wave of qpKdV equation
    • Hong J., and Liu Y. Multi-symplecticity of the centred box discretization for a class of Hamiltonian PDEs and an application to quasi-periodically solitary wave of qpKdV equation. Math. Comput. Model. 39 (2004) 1035-1047
    • (2004) Math. Comput. Model. , vol.39 , pp. 1035-1047
    • Hong, J.1    Liu, Y.2
  • 9
    • 33645984826 scopus 로고    scopus 로고
    • Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
    • Hong J., Liu Y., Munthe-Kaas H., and Zanna A. Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients. Appl. Numer. Math. 56 (2006) 814-843
    • (2006) Appl. Numer. Math. , vol.56 , pp. 814-843
    • Hong, J.1    Liu, Y.2    Munthe-Kaas, H.3    Zanna, A.4
  • 10
    • 85009774577 scopus 로고    scopus 로고
    • The Multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
    • Hong J., Liu H., and Sun G. The Multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs. Math. Comput. 75 (2006) 167-181
    • (2006) Math. Comput. , vol.75 , pp. 167-181
    • Hong, J.1    Liu, H.2    Sun, G.3
  • 11
    • 26944495302 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
    • Hong J., and Li C. Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations. J. Comput. Phys. 211 (2006) 448-472
    • (2006) J. Comput. Phys. , vol.211 , pp. 448-472
    • Hong, J.1    Li, C.2
  • 13
    • 0035841060 scopus 로고    scopus 로고
    • Geometric integrators for the nonlinear Schrödinger equation
    • Islas A.L., Karpeev D.A., and Schober C.M. Geometric integrators for the nonlinear Schrödinger equation. J. Comput. Phys. 173 (2001) 116-148
    • (2001) J. Comput. Phys. , vol.173 , pp. 116-148
    • Islas, A.L.1    Karpeev, D.A.2    Schober, C.M.3
  • 14
    • 3242702916 scopus 로고    scopus 로고
    • On the preservation of phase space structure under multisymplectic discretization
    • Islas A.L., and Schober C.M. On the preservation of phase space structure under multisymplectic discretization. J. Comput. Phys. 197 (2004) 585-609
    • (2004) J. Comput. Phys. , vol.197 , pp. 585-609
    • Islas, A.L.1    Schober, C.M.2
  • 17
    • 0037400145 scopus 로고    scopus 로고
    • Multisymplectic integration methods for Hamiltonian PDEs
    • Moore B., and Reich S. Multisymplectic integration methods for Hamiltonian PDEs. Future Gener. Comput. Syst. 19 (2003) 395-402
    • (2003) Future Gener. Comput. Syst. , vol.19 , pp. 395-402
    • Moore, B.1    Reich, S.2
  • 18
    • 0242339583 scopus 로고    scopus 로고
    • Backward error analysis for multi-symplectic integration methods
    • Moore B., and Reich S. Backward error analysis for multi-symplectic integration methods. Numer. Math. 95 (2003) 625-652
    • (2003) Numer. Math. , vol.95 , pp. 625-652
    • Moore, B.1    Reich, S.2
  • 19
    • 0034687898 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equation
    • Reich S. Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equation. J. Comput. Phys. 157 (2000) 473-499
    • (2000) J. Comput. Phys. , vol.157 , pp. 473-499
    • Reich, S.1
  • 21
    • 0034319701 scopus 로고    scopus 로고
    • Novel soliton solutions of the nonlinear Schrödinger equation model
    • Serkin V.N., and Hasegawa A. Novel soliton solutions of the nonlinear Schrödinger equation model. Phys. Rev. Lett. 85 (2000) 4502-4505
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 4502-4505
    • Serkin, V.N.1    Hasegawa, A.2
  • 22
    • 0042475779 scopus 로고
    • On the conservation of the symplectic structure in the numerical solution of Hamiltonian systems (in Russian)
    • Numerical Solution of Ordinary Differential Equations. Filippov S.S. (Ed), USSR Academy of Sciences, Moscow
    • Suris Y.B. On the conservation of the symplectic structure in the numerical solution of Hamiltonian systems (in Russian). In: Filippov S.S. (Ed). Numerical Solution of Ordinary Differential Equations. Keldysh Institute of Applied Mathematics (1988), USSR Academy of Sciences, Moscow 148-160
    • (1988) Keldysh Institute of Applied Mathematics , pp. 148-160
    • Suris, Y.B.1
  • 23
    • 0038041190 scopus 로고
    • The canonicity of mapping generated by Runge-Kutta type methods when integrating the systems over(x, ̈) = - ∂ U / ∂ x
    • Suris Y.B. The canonicity of mapping generated by Runge-Kutta type methods when integrating the systems over(x, ̈) = - ∂ U / ∂ x. Zh. Vychisl. Mat. i Mat. Fiz. 29 (1989) 138-144
    • (1989) Zh. Vychisl. Mat. i Mat. Fiz. , vol.29 , pp. 138-144
    • Suris, Y.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.