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An extension of the Hamilton-Jacobi method. (English. Russian original) Zbl 1257.58025
Dokl. Math. 85, No. 2, 301-303 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 443, No. 5, 561-563 (2012).
The note under review provides an extension of the Hamilton-Jacobi theory to the problem of finding invariant manifolds of Hamiltonian differential equations.
MSC:
58J70 Invariance and symmetry properties for PDEs on manifolds
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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References:
[1] V. V. Kozlov, General Theory of Vortices (Udmurtskii Univ., Izhevsk, 1998; Springer-Verlag, Berlin, 2003).
[2] Lamb, H., Hydrodynamics (Dover, New York, 1945; Gostekhizdat, Moscow, 1947). · Zbl 0828.01012
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