On the Smoothness of the Time t Map of the KdV Equation and the Bifurcation of the Eigenvalues of Hill's Operator

Ratiu, T.

doi:10.1007/BFb0069808

On the Smoothness of the Time t Map of the KdV Equation and the Bifurcation of the Eigenvalues of Hill's Operator

T. Ratiu
(
- UC, Berkeley
)

1978

47 pages

Part of GLOBAL ANALYSIS. PROCEEDINGS OF THE BIENNIAL SEMINAR OF THE CANADIAN MATHEMATICAL CONGRESS, CALGARY, ALBERTA, JUNE 12-27, 1978, 248-294

Published in:

Lect.Notes Math. 755 (1979) 248-294

Contribution to:

Biennial Seminar of The Canadian Mathematical Congress, 248-294

DOI:

10.1007/BFb0069808

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LECTURES
FIELD THEORY: CLASSICAL
FIELD EQUATIONS: NONLINEAR
Korteweg-de Vries equation
FIELD EQUATIONS: SOLITON
INVERSE SCATTERING METHOD
GROUP THEORY: LIE
ALGEBRA: LIE
MATHEMATICAL METHODS

References(30)

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: Foundations of Mechanics, Second Edition

R. Abraham
,
J. Marsden

: On the relationship of some results of Gelfand-Dikii and P. van Moerbeke, and a natural trace functional for formal asymptotic pseudo-differential operators, preprint, to appear in Inventiones Math

M. Adler

: On a trace functional for formal pseudo-differential operators and the Hamiltonian structure of Korteweg-deVries type equations (this volume)

M. Adler

Completely integrable Moody Hamiltonian Systems (In preparation)

M. Adler
,
P. van Moerbeke

: Genericity of Simple Eigenvalues, preprint, University of Utah, Salt Lake City

R. Carlson

: Product formulas and numerical algorithms, Comm. Pure and Applied Math. Vol XXXI, p. 205-256

A. Chorin
,
T. Hughes
,
M. McCracken
,
J. Marsden

MathSciNetCrossRefzbMATHGoogle Scholar

: Inverse scattering on the line, to appear

P. Deift
,
E. Trubowitz

: Groups of diffeomorphisms and the motion of an incompressible fluid

D. Ebin
,
J. Marsden

- Annals Math. 92 (1970) 102-163

: The Korteweg-de Vries Equation, a completely integrable Hamiltonian system (in Russian)

L. Fadeev
,
V. Zakharov

- Funct.Anal.Appl. 5 (1971) 18-27

: Quasi-linear equations of evolution, with applications to partial differential equations, in Spectral Theory and Differential Equations, Lecture Notes in Mathematics, #448 Verlag

T. Kato

____: The Cauchy problem for quasi-linear symmetric hyperbolic systems

- Arch.Ration.Mech.Anal. 58 (1975) 181-205

____: Linear and quasi-linear equations of evolution of hyperbolic type, CIME, Bressanone

: Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure and Applied Math., Vol. XXXI, p. 481-507

J. Kazhdan
,
B. Kostant
,
S. Sternberg

: Dynkin diagrams and the generalized Toda lattice, preprint

B. Kostant

: Hill's equation, New York

W. Magnus
,
W. Winkler

: (this volume)

H. McKean

: The spectrum of Hill's equation, Inventiones Math. 30, p. 217-274

H. McKean
,
P. van Moerbeke

: Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points, Comm. Pure and Applied Math. Vol. XXIX, p. 143-226

H. McKean
,
E. Trubowitz

: A remark on semigroups depending smoothly on a parameter, unpublished preprint, Berkeley

J. Marsden

____: On product formulas for nonlinear semigroups

- J.Funct.Anal. 13 (1973) 51-72

____: Applications of Global Analysis for Mathematical Physics, Publish or Perish

____: Qualitative Methods in Bifurcation Theory

- Bull.Am.Math.Soc. 84 (1978) 1125-1148

: The Hopf bifurcation and its applications Applied Math. Sciences #19

J. Marsden
,
M. McCracken

: The theory of one-dimensional Schrödinger operators with a periodic potential, Journal of Math

N. Meimann

- APS Physics 18 (1977) 834-848

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