Affiliation:
1. School of Mathematics , Southeast University , Nanjing, Jiangsu 210096 , P.R. China
Abstract
Abstract
The mixed Kaup-Newell (mKN) hierarchy, including the nonholonomic deformation of the KN equation, is obtained in the Lenard scheme. By the nonlinearisation of the Lax pair, the mKN hierarchy is reduced to a family of mixed, finite-dimensional Hamiltonian systems (FDHSs) that separate its temporal and spatial variables. It turns out that the Bargmann map not only gives rise to the finite parametric solutions of the mKN hierarchy but also specifies a finite-dimensional, invariant subspace for the mKN flows. The Abel-Jacobi variables are selected to linearise the mKN flows on the Jacobi variety of a Riemann surface, from which some quasi-periodic solutions of mKN hierarchy are presented by using the Riemann-Jacobi inversion.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
Reference44 articles.
1. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia 1981.
2. S. P. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons, the Inverse Scattering Methods, Consultants Bureau, New York 1984.
3. A. C. Newell, Solitons in Mathematics and Physics, SIAM, Philadelphia 1985.
4. P. D. Lax, Commun. Pure Appl. Math. 21, 467 (1968).
5. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, Berlin 1978.
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