References
Gel'fand, I.M., Dikii, L.A.: Fractional Powers of Operators and Hamiltonian Systems. Funkcional'nyi Analiz i ego Prilozenija,10, No. 4 (1976)
van Moerbeke, P.: The Floquet Theory for Periodic Jacobi Matrices. Inventiones Mat.37, Fasc. 1 (1976)
Lax, P.: Almost Periodic Solutions of the KDV Equation. SIAM Reviews, 1976
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)
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)
McKean, H.P.: Boussinesq's Equation as a Hamiltonian System. To appear in a volume dedicated to M.G. Krein on his Seventieth birthday
Seeley, R.: Complex Powers of an Elliptic Operator. Proceedings of Symposia in Pure Mathematics,10, AMS (1967)
Symes, B.: To appear as MRC Technical Report. University of Wisconsin-Madison, 1978
Moser, J.: Three Integrable Hamiltonian Systems Connected with Isospectral Deformations. Adv. in Math.,16, No. 2 (1975)
Adler, M.: Some Finite Dimensional Systems and their Scattering Behavior. Comm. Math. Physics,55 (1977)
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)
Mardsen, J.: Applications of Global Analysis in Mathematical Physics. Publish or Petish, Inc., Chap. 6 (1974)
Kazhdan, D., Kostant, B., Sternberg, S.: Hamiltonian Group Actions and Dynamical Systems of Calogero Type. C.P.A.M. (1978)
Adler, M.: Completely Integrable Systems and Symplectic Actions. MRC Technical Summary Report #1830, University of Wisconsin-Madison, in press (1978)
Dikii, L.: Hamiltonian Systems Connected with the Rotation Group. Funkcional 'nyi Analiz i ego Prilozenija,6, 83–84 (1972)
Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press Inc. (1972)
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)
Kirillov, A.A.: Elements of the Theory of Representations. Berlin, Heidelberg, New York: Springer-Verlag pp. 226–235, 290–292, 1976
Gel'fand, I.M., Dikii, L.A.: The Resolvent and Hamiltonian Systems. Funkcional'nyi Analiz i ego Prilozenija,11, 11–27 (1977)
Guillemin, V., Quillen, D., Sternberg, S.: The Integrability of Characteristics. C.P.A.M.23, 39–77 (1970)
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
Flaschka, H.: On the Toda lattice I. Phys. Rev. B9, 1924–1925 (1974)
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)
Lax, P.D.: Integrals of Nonlinear Equations of Evolution and Solitary Waves. Comm. Pure Appl. Math.,21, 467–490 (1968)
Bogoyavlensky, O.I.: On Perturbations of the Periodic Toda Lattices. Comm. Math. Physics.,51, 201–209 (1976)
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)
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01410079