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Volumn 7, Issue 3, 2010, Pages 613-630

Novel multi-symplectic integrators for nonlinear fourth-order Schrödinger equation with trapped term

Author keywords

Conservation law; Fourier spectral method; Multi symplectic scheme; Schr dinger equation with trapped term; Split step method

Indexed keywords


EID: 77949753473     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.2009.09.057     Document Type: Article
Times cited : (37)

References (28)
  • 1
    • 0001417067 scopus 로고    scopus 로고
    • Stabilization of soliton instabilities by higher-order dispersion: Fourth order nonlinear Schrödinger-type equations
    • V.I. Karpman, Stabilization of soliton instabilities by higher-order dispersion: Fourth order nonlinear Schrödinger-type equations, Phys. Rev. E 53 (1996) 1336-339.
    • (1996) Phys. Rev. E , vol.53 , pp. 1336-1339
    • Karpman, V.I.1
  • 2
    • 0039592594 scopus 로고    scopus 로고
    • Stability of soliton described by nonlinear Schrödinger-type equations with higher-order dispersion
    • V.I. Karpman, A.G. Shagalov, Stability of soliton described by nonlinear Schrödinger-type equations with higher-order dispersion. Physica. D 144 (2000) 194-210.
    • (2000) Physica. D , vol.144 , pp. 194-210
    • Karpman, V.I.1    Shagalov, A.G.2
  • 3
    • 62049085138 scopus 로고    scopus 로고
    • The cubic fourth-order Schrödinger equation
    • B. Pausader, The cubic fourth-order Schrödinger equation. J. Func. Anal. 256 (2009) 2473- 2517.
    • (2009) J. Func. Anal. , vol.256 , pp. 2473-2517
    • Pausader, B.1
  • 4
    • 0015671259 scopus 로고
    • The Soilton: A new concept in applied science
    • A.C. Scott, F.Y. Chu, D.W. Mciaughhn, The Soilton: a new concept in applied science, Proc. IEEE. 61 (1973) 1443-1483.
    • (1973) Proc. IEEE , vol.61 , pp. 1443-1483
    • Scott, A.C.1    Chu, F.Y.2    Mciaughhn, D.W.3
  • 5
    • 0037774726 scopus 로고    scopus 로고
    • Numerical methods for the simulation of a trapped nonlinear Schrödinger system
    • V.M. Pérez-García, X.Y. Liu, Numerical methods for the simulation of a trapped nonlinear Schrödinger system. Appl. Math. Comput. 144 (2003) 215-235.
    • (2003) Appl. Math. Comput. , vol.144 , pp. 215-235
    • Pérez-García, V.M.1    Liu, X.Y.2
  • 6
    • 12344307063 scopus 로고
    • A difference scheme for a class of nonlinear Schrödinger equation
    • H.Y. Chao. A difference scheme for a class of nonlinear Schrödinger equation. J. Comput. Math. 5 (1987) 272-280.
    • (1987) J. Comput. Math. , vol.5 , pp. 272-280
    • Chao, H.Y.1
  • 7
    • 33746113364 scopus 로고    scopus 로고
    • A leap frog finite difference scheme for a class of nonlinear Schrödinger equations of high order
    • W.P. Zeng, A leap frog finite difference scheme for a class of nonlinear Schrödinger equations of high order. J. Comput. Math. 17 (1999) 133-138.
    • (1999) J. Comput. Math. , vol.17 , pp. 133-138
    • Zeng, W.P.1
  • 8
    • 77949739026 scopus 로고    scopus 로고
    • Symplectic geometric algorithms for Hamiltonian system
    • Press of Zhejiang: Hangzhou (in Chinese
    • K. Feng, M. Qin, Symplectic geometric algorithms for Hamiltonian system. Sci. and Tech. Press of Zhejiang: Hangzhou (in Chinese), 2002.
    • (2002) Sci. and Tech.
    • Feng, K.1    Qin, M.2
  • 10
    • 34547507895 scopus 로고    scopus 로고
    • Recent progress in symplectic algorithms for use in quantum systems
    • X. Liu, Y. Qi, J. He, P. Ding, Recent progress in symplectic algorithms for use in quantum systems. Commun. Comput. Phys. 2 (2007) 1-53.
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 1-53
    • Liu, X.1    Qi, Y.2    He, J.3    Ding, P.4
  • 11
    • 67650941643 scopus 로고    scopus 로고
    • Explicit symplectic methods for the nonlinear Schrödinger equation
    • H. Guan, Y. Jiao, J. Liu, Y. Tang, Explicit symplectic methods for the nonlinear Schrödinger equation. Commun. Comput. Phys. 6 (2009) 639-654.
    • (2009) Commun. Comput. Phys. , vol.6 , pp. 639-654
    • Guan, H.1    Jiao, Y.2    Liu, J.3    Tang, Y.4
  • 12
    • 48249133292 scopus 로고    scopus 로고
    • Long-term numerical simulation of the interaction between a neutron field and a neutral meson field by a symplectic-preserving scheme
    • L. Kong, J. Hong, R. Liu, Long-term numerical simulation of the interaction between a neutron field and a neutral meson field by a symplectic-preserving scheme. J. Phys. A: Math. Theor. 41 (2008) 255207.
    • (2008) J. Phys. A: Math. Theor. , vol.41 , pp. 255207
    • Kong, L.1    Hong, J.2    Liu, R.3
  • 13
    • 0034687898 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equation
    • S. Reich, 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
  • 14
    • 0037832748 scopus 로고    scopus 로고
    • Multi-symplectic integrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity
    • T.J. Bridges, S. Reich, Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A 284 (2001) 184-193.
    • (2001) Phys. Lett. a , vol.284 , pp. 184-193
    • Bridges, T.J.1    Reich, S.2
  • 15
    • 0039152065 scopus 로고    scopus 로고
    • Multi-symplectic spectral discretization for the Zakharov-Kuznetsov and shallow water equations
    • T.J. Bridges, S. Reich, Multi-symplectic spectral discretization for the Zakharov-Kuznetsov and shallow water equations. Physica D 152 (2001) 491-504.
    • (2001) Physica D , vol.152 , pp. 491-504
    • Bridges, T.J.1    Reich, S.2
  • 16
    • 33645984826 scopus 로고    scopus 로고
    • Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
    • J. Hong, Y. Liu, Hans Munthe-Kaas, Antonella Zanna, 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
  • 17
    • 34548697286 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients
    • J. Hong, X. Liu, C. Li, Multi-symplectic Runge-Kutta-Nyström methods for nonlinear Schrödinger equations with variable coefficients. J. Comput. Phys. 226 (2007) 1968-1984.
    • (2007) J. Comput. Phys. , vol.226 , pp. 1968-1984
    • Hong, J.1    Liu, X.2    Li, C.3
  • 18
    • 38849102343 scopus 로고    scopus 로고
    • Explicit multi-symplectic methods for Hamiltonian wave equations
    • J. Hong, S. Jiang, C. Li, H. Liu, Explicit multi-symplectic methods for Hamiltonian wave equations. Commun. Comput. Phys. 2 (2007) 662-683.
    • (2007) Commun. Comput. Phys. , vol.2 , pp. 662-683
    • Hong, J.1    Jiang, S.2    Li, C.3    Liu, H.4
  • 19
    • 34547553661 scopus 로고    scopus 로고
    • On multi-symplecticity of partitioned Runge-Kutta and splitting methods
    • B.N. Ryland, B.I. McLachlan, J. Frank, On multi-symplecticity of partitioned Runge-Kutta and splitting methods. Inter. J. Comput. Math. 84 (2007) 847-869.
    • (2007) Inter. J. Comput. Math. , vol.84 , pp. 847-869
    • Ryland, B.N.1    Mclachlan, B.I.2    Frank, J.3
  • 20
    • 26944495302 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
    • J. Hong, C. Li, 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
  • 22
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic equations
    • D. Peaceman, H. Rachford, The numerical solution of parabolic and elliptic equations, J. Soc. Indust. Appl. Math. 3 (1955) 28-41.
    • (1955) J. Soc. Indust. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.1    Rachford, H.2
  • 23
    • 84967782959 scopus 로고
    • On the numerical solution of heat conduction problems in two and three space variables
    • J. Douglas Jr, H.H. Rachford Jr, On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc. 82 (1956) 421-439.
    • (1956) Trans. Amer. Math. Soc. , vol.82 , pp. 421-439
    • Douglas Jr., J.1    Rachford Jr., H.H.2
  • 24
    • 0000251609 scopus 로고
    • Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method
    • A.C. Newell (Ed.), Providence, RI
    • F. Tappert, Numerical solutions of the Korteweg-de Vries equation and its generalizations by the split-step Fourier method. in: A.C. Newell (Ed.), Nonlinear Wave Motion, Lect. Appl. Math., Amer. Math. Soc., Providence, RI, 15, (1974) 215-216.
    • (1974) Nonlinear Wave Motion, Lect. Appl. Math., Amer. Math. Soc. , vol.15 , pp. 215-216
    • Tappert, F.1
  • 25
    • 0001518684 scopus 로고
    • On the construction and comparison of difference scheme
    • G. Strang, On the construction and comparison of difference scheme. SIAM J.Numer. Anal. 5 (1968) 506-517.
    • (1968) SIAM J.Numer. Anal. , vol.5 , pp. 506-517
    • Strang, G.1
  • 26
    • 33748077411 scopus 로고    scopus 로고
    • Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations
    • Z.L. Xu, J.S. He, H.D. Han, Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations. Appl. Math. Comput. 179 (2006) 596-605.
    • (2006) Appl. Math. Comput. , vol.179 , pp. 596-605
    • Xu, Z.L.1    He, J.S.2    Han, H.D.3
  • 27
    • 77954626424 scopus 로고    scopus 로고
    • Numerical studies on Boussinesq-type equations via a split-step Fourier method
    • DOI: 10.1080/00207160802464597
    • L. Kong, L.Wang, Numerical studies on Boussinesq-type equations via a split-step Fourier method, Inter. J. Comput. Math., DOI: 10.1080/ 00207160802464597.
    • Inter. J. Comput. Math.
    • Kong, L.1    Wang, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.