Abstract
The equations
have several remarkable features in common, among them
-
(i)
a Hamiltonian structure.
-
(ii)
an infinite number of conservation laws; all of them Hamiltonians in involution.
-
(iii)
an associated spectral problem, invariant under the flow.
-
(iv)
solvability by inverse scattering method.
In addition to the above three examples there are entire hierarchies of such “completely integrable Hamiltonian systems” based on any semi-simple Lie algebra. In this section we shall explain these ideas and give some further examples.
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© 1986 Springer-Verlag Berlin Heidelberg
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Sattinger, D.H., Weaver, O.L. (1986). Applications. In: Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics. Applied Mathematical Sciences, vol 61. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1910-9_14
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DOI: https://doi.org/10.1007/978-1-4757-1910-9_14
Publisher Name: Springer, New York, NY
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