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On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations. (English) Zbl 0393.35058

35Q99 Partial differential equations of mathematical physics and other areas of application
35S99 Pseudodifferential operators and other generalizations of partial differential operators
70H99 Hamiltonian and Lagrangian mechanics
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[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) · Zbl 0361.15010
[3] Lax, P.: Almost Periodic Solutions of the KDV Equation. SIAM Reviews, 1976 · Zbl 0329.35015
[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)
[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 · Zbl 0546.58022
[7] Seeley, R.: Complex Powers of an Elliptic Operator. Proceedings of Symposia in Pure Mathematics,10, AMS (1967) · Zbl 0159.15504
[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) · Zbl 0303.34019
[10] Adler, M.: Some Finite Dimensional Systems and their Scattering Behavior. Comm. Math. Physics,55 (1977) · Zbl 0366.58004
[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) · Zbl 0368.58008
[14] Adler, M.: Completely Integrable Systems and Symplectic Actions. MRC Technical Summary Report #1830, University of Wisconsin-Madison, in press (1978) · Zbl 0414.58020
[15] Dikii, L.: Hamiltonian Systems Connected with the Rotation Group. Funkcional ’nyi Analiz i ego Prilozenija,6, 83-84 (1972)
[16] Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press Inc. (1972) · Zbl 0242.42001
[17] van Moerbeke, P.: The spectrum of Operators and Algebraic Geometry-Lecture delivered at Strasbourg (SĂ©minaire 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
[19] Gel’fand, I.M., Dikii, L.A.: The Resolvent and Hamiltonian Systems. Funkcional’nyi Analiz i ego Prilozenija,11, 11-27 (1977)
[20] Guillemin, V., Quillen, D., Sternberg, S.: The Integrability of Characteristics. C.P.A.M.23, 39-77 (1970) · Zbl 0203.33002
[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) · Zbl 0942.37504 · doi:10.1103/PhysRevB.9.1924
[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) · Zbl 0291.35012 · doi:10.1002/cpa.3160270108
[24] Lax, P.D.: Integrals of Nonlinear Equations of Evolution and Solitary Waves. Comm. Pure Appl. Math.,21, 467-490 (1968) · Zbl 0162.41103 · doi:10.1002/cpa.3160210503
[25] Bogoyavlensky, O.I.: On Perturbations of the Periodic Toda Lattices. Comm. Math. Physics.,51, 201-209 (1976) · doi:10.1007/BF01617919
[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)
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