Letters in Mathematical Physics

, Volume 79, Issue 2, pp 213–220 | Cite as

Multisymplectic Structures and Discretizations for One-way Wave Equations



Multisymplectic structures for one-way wave equations are presented in this letter. Based on the multisymplectic formulation, we obtain the corresponding multisymplectic discretizations. The structure-preserving property of a finite difference scheme for the first-order one-way wave equation is proved. Implications and applications of this result are explored.

Mathematics Subject Classification (2000)

70G45 70S10 


multisymplectic discretization one-way equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alford R.M., Kelley K.R., Boore D.M. (1974) Accuracy of finite difference modeling of the acoustic wave equation. Geophysics 39, 834–842CrossRefGoogle Scholar
  2. 2.
    Bridges T.J., Reich S. (2001) Multisymplectic integrators: integrators for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A 284, 184–193MATHCrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Chen J.B. (2001) New schemes for the nonlinear Schrödinger equation. Appl. Math. Comp. 124, 371–379MATHCrossRefGoogle Scholar
  4. 4.
    Chen J.B. (2002) Multisymplecticity of Crank-Nicolson scheme for the nonlinear Schrödinger equation. J. Phys. Soc. J. 71, 2348–2349MATHCrossRefGoogle Scholar
  5. 5.
    Chen J.B. (2002) Total variation in discrete multisymplectic field theory and multisymplectic energy momentum integrators. Lett. Math. Phys. 61, 63–73MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen J.B. (2003) Multisymplectic geometry, local conservation laws and a multisymplectic integrator for the Zakharov-Kuznetsov equation. Lett. Math. Phys. 63, 115–124MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Claerbout J.F. (1985) Imaging the Earth’s Interior. Blackwell, OxfordGoogle Scholar
  8. 8.
    Ma Z.T. (1989) Seismic imaging techniques: finite-difference migration. Oil Industry Press, BeijingGoogle Scholar
  9. 9.
    Reich S. (2000) Multisymplectic Runge-Kutta collocation methods for Hamiltonian wave equations. J. Comp. Phys. 157, 473–499MATHCrossRefADSGoogle Scholar
  10. 10.
    Ristow D., Rühl T. (1997) 3-D implicit finite-difference migration by multiway splitting. Geophysics 62, 554–567CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina

Personalised recommendations