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The constraints of potentials and the finite-dimensional integrable systems. (English) Zbl 0695.58016

Summary: Restricting potential to the space spanned by the eigenvectors of the recursion operator leads to a natural constraint of potential and a finite-dimensional integrable Hamiltonian system. The general method for proving the consistency of the two systems stemming from the Lax pair and obtaining the constants of the motion fo the Hamiltonian system is illustrated by the classical Boussinesq and AKNS hierarchies. By using gauge transformation, similar results for the Jaulent-Miodek and Kaup- Newell hierarchies are presented.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q99 Partial differential equations of mathematical physics and other areas of application
58D25 Equations in function spaces; evolution equations
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
81T08 Constructive quantum field theory
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References:

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