Skip to main content
SpringerLink
Log in

On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Gel'fand, I.M., Dikii, L.A.: Fractional Powers of Operators and Hamiltonian Systems. Funkcional'nyi Analiz i ego Prilozenija,10, No. 4 (1976)

  2. van Moerbeke, P.: The Floquet Theory for Periodic Jacobi Matrices. Inventiones Mat.37, Fasc. 1 (1976)

    Google Scholar 

  3. Lax, P.: Almost Periodic Solutions of the KDV Equation. SIAM Reviews, 1976

  4. Gel'fand, I.M., Mann, Yu.I., Shubin, M.A.: Poisson Brackets and the Kernel of a Variational Derivative in Formal Variational Calculus. Funkts. Anal. Prilozen.,10, No. 4 (1976)

    Google Scholar 

  5. Adler, M.: Some Algebraic Relations Common to a Set of Integrable Partial and Ordinary Differential Equations. MRC Technical Report #1801, University of Wisconsin-Madison (1977)

  6. McKean, H.P.: Boussinesq's Equation as a Hamiltonian System. To appear in a volume dedicated to M.G. Krein on his Seventieth birthday

  7. Seeley, R.: Complex Powers of an Elliptic Operator. Proceedings of Symposia in Pure Mathematics,10, AMS (1967)

  8. Symes, B.: To appear as MRC Technical Report. University of Wisconsin-Madison, 1978

  9. Moser, J.: Three Integrable Hamiltonian Systems Connected with Isospectral Deformations. Adv. in Math.,16, No. 2 (1975)

  10. Adler, M.: Some Finite Dimensional Systems and their Scattering Behavior. Comm. Math. Physics,55 (1977)

  11. Arnold, V.: Sur la geometric differentielle des groups de Lie de dimension infinite et ses applications a l'hydrodynamique des fluids parfaits. Ann. Inst. Grenoble,16 (1) (1966)

  12. Mardsen, J.: Applications of Global Analysis in Mathematical Physics. Publish or Petish, Inc., Chap. 6 (1974)

  13. Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian Group Actions and Dynamical Systems of Calogero Type. C.P.A.M. (1978)

  14. Adler, M.: Completely Integrable Systems and Symplectic Actions. MRC Technical Summary Report #1830, University of Wisconsin-Madison, in press (1978)

  15. Dikii, L.: Hamiltonian Systems Connected with the Rotation Group. Funkcional 'nyi Analiz i ego Prilozenija,6, 83–84 (1972)

    Google Scholar 

  16. Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press Inc. (1972)

  17. van Moerbeke, P.: The spectrum of Operators and Algebraic Geometry-Lecture delivered at Strasbourg (Séminaire Leray-Ramis). To appear in Springer-Verlag Lecture Notes (1977)

  18. Kirillov, A.A.: Elements of the Theory of Representations. Berlin, Heidelberg, New York: Springer-Verlag pp. 226–235, 290–292, 1976

    Google Scholar 

  19. Gel'fand, I.M., Dikii, L.A.: The Resolvent and Hamiltonian Systems. Funkcional'nyi Analiz i ego Prilozenija,11, 11–27 (1977)

    Google Scholar 

  20. Guillemin, V., Quillen, D., Sternberg, S.: The Integrability of Characteristics. C.P.A.M.23, 39–77 (1970)

    Google Scholar 

  21. Moser, J.: Finitely Many Mass Points on the Line under the influence of an Exponential Potential — an Integrable System. Lecture Notes in Physics-Dynamical Systems, Theory and Application (J. Moser, ed.) pp. 467–498, 1975

  22. Flaschka, H.: On the Toda lattice I. Phys. Rev. B9, 1924–1925 (1974)

    Google Scholar 

  23. Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Korteweg-deVries Equation and Generalizations VI, Methods of Exact Solution. Comm. Pure Appl. Math.,27, 97–133 (1974)

    Google Scholar 

  24. Lax, P.D.: Integrals of Nonlinear Equations of Evolution and Solitary Waves. Comm. Pure Appl. Math.,21, 467–490 (1968)

    Google Scholar 

  25. Bogoyavlensky, O.I.: On Perturbations of the Periodic Toda Lattices. Comm. Math. Physics.,51, 201–209 (1976)

    Google Scholar 

  26. Adler, M.: On a Trace Functional for Formal Pseudo-Differential Operators and The Hamiltonian Structure of the Korteweg de Vries Type Equations, to appear in Proceeding of the Calgary Conference on Global Analysis of June 1978, Springer Lecture Notes (1979)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Minnesota, 55455, Minneapolis, Minn., USA

    M. Adler

Authors
  1. M. Adler
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and the National Science Foundation under Grand No. MCS75-17385A01

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adler, M. On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-devries type equations. Invent Math 50, 219–248 (1978). https://doi.org/10.1007/BF01410079

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01410079

Keywords

Search

Navigation