Inventiones mathematicae

, Volume 50, Issue 3, pp 219–248 | Cite as

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

  • M. Adler
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)Google Scholar
  2. 2.
    van Moerbeke, P.: The Floquet Theory for Periodic Jacobi Matrices. Inventiones Mat.37, Fasc. 1 (1976)Google Scholar
  3. 3.
    Lax, P.: Almost Periodic Solutions of the KDV Equation. SIAM Reviews, 1976Google Scholar
  4. 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. 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)Google Scholar
  6. 6.
    McKean, H.P.: Boussinesq's Equation as a Hamiltonian System. To appear in a volume dedicated to M.G. Krein on his Seventieth birthdayGoogle Scholar
  7. 7.
    Seeley, R.: Complex Powers of an Elliptic Operator. Proceedings of Symposia in Pure Mathematics,10, AMS (1967)Google Scholar
  8. 8.
    Symes, B.: To appear as MRC Technical Report. University of Wisconsin-Madison, 1978Google Scholar
  9. 9.
    Moser, J.: Three Integrable Hamiltonian Systems Connected with Isospectral Deformations. Adv. in Math.,16, No. 2 (1975)Google Scholar
  10. 10.
    Adler, M.: Some Finite Dimensional Systems and their Scattering Behavior. Comm. Math. Physics,55 (1977)Google Scholar
  11. 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)Google Scholar
  12. 12.
    Mardsen, J.: Applications of Global Analysis in Mathematical Physics. Publish or Petish, Inc., Chap. 6 (1974)Google Scholar
  13. 13.
    Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian Group Actions and Dynamical Systems of Calogero Type. C.P.A.M. (1978)Google Scholar
  14. 14.
    Adler, M.: Completely Integrable Systems and Symplectic Actions. MRC Technical Summary Report #1830, University of Wisconsin-Madison, in press (1978)Google Scholar
  15. 15.
    Dikii, L.: Hamiltonian Systems Connected with the Rotation Group. Funkcional 'nyi Analiz i ego Prilozenija,6, 83–84 (1972)Google Scholar
  16. 16.
    Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press Inc. (1972)Google Scholar
  17. 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)Google Scholar
  18. 18.
    Kirillov, A.A.: Elements of the Theory of Representations. Berlin, Heidelberg, New York: Springer-Verlag pp. 226–235, 290–292, 1976Google Scholar
  19. 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. 20.
    Guillemin, V., Quillen, D., Sternberg, S.: The Integrability of Characteristics. C.P.A.M.23, 39–77 (1970)Google Scholar
  21. 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, 1975Google Scholar
  22. 22.
    Flaschka, H.: On the Toda lattice I. Phys. Rev. B9, 1924–1925 (1974)Google Scholar
  23. 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. 24.
    Lax, P.D.: Integrals of Nonlinear Equations of Evolution and Solitary Waves. Comm. Pure Appl. Math.,21, 467–490 (1968)Google Scholar
  25. 25.
    Bogoyavlensky, O.I.: On Perturbations of the Periodic Toda Lattices. Comm. Math. Physics.,51, 201–209 (1976)Google Scholar
  26. 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)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • M. Adler
    • 1
  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations