Skip to main content
Log in

Variational Formulation for the Multisymplectic Hamiltonian Systems

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

A variational formulation for the multisymplectic Hamiltonian systems is presented in this Letter. Using this variational formulation, we obtain multisymplectic integrators from a variational perspective. Numerical experiments are also reported.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T.J. Bridges (1997) ArticleTitleMulti-symplectic structures and wave propagation Math. Proc. Cam. Phil. Sob. 121 147–190

    Google Scholar 

  2. T.J. Bridges S. Reich (2001) ArticleTitleMulti-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity Phys. Lett. A 284 184–193

    Google Scholar 

  3. J.B. Chen (2002) ArticleTitleTotal variation in discrete multisymplectic field theory and multisymplectic energy momentum integrators Lett. Math. Phys. 61 63–73

    Google Scholar 

  4. J.B. Chen (2003) ArticleTitleMultisymplectic geometry, local conservation laws and a multisymplectic integrator for the Zakharov–Kuznetsov equation Lett. Math. Phys. 63 115–124

    Google Scholar 

  5. J.B. Chen H.Y. Guo K. Wu (2003) ArticleTitleTotal variation in Hamiltonian formalism and symplectic-energy integrators J. Math. Phys. 44 1688–1702

    Google Scholar 

  6. H.Y. Guo Y.Q. Li K. Wu (2001) ArticleTitleOn symplectic and multisymplectic structures and their discrete versions in Lagrangian formalism Comm. Theor. Phys. 35 703–710

    Google Scholar 

  7. J.E. Marsden G.W. Patrick S. Shkoller (1998) ArticleTitleMultisymplectic geometry, variational integrators, and nonlinear PDEs Comm. Math. Phys. 199 351–395

    Google Scholar 

  8. P.J. Olver (1993) Applications of Lie groups to differential equations EditionNumber2 Springer-Verlag New York

    Google Scholar 

  9. S. Reich (2000) ArticleTitleMulti-symplectic Runge–Kutta collocation methods for Hamiltonian wave equations J. Comput. Phys. 157 473–499

    Google Scholar 

  10. P.F. Zhao M.Z. Qin (2000) ArticleTitleMultisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation J. Phys. A: Math Gen. 33 3613–3626

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jing-Bo Chen.

Additional information

Mathematical Subject Classifications (2000). 70G50, 58Z05.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, JB. Variational Formulation for the Multisymplectic Hamiltonian Systems. Lett Math Phys 71, 243–253 (2005). https://doi.org/10.1007/s11005-005-1813-9

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-005-1813-9

Keywords

Navigation