Vus A. Interaction potentials of Liouville integrable many-particle systems on the line

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0402U003735

Thesis Registration Form

0402U003735.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

21-11-2002

Specialized Academic Board

К 35.051.07

Essay

In the thesis the problems of the Liouville integrability of Hamiltonian dynamical systems are considered for the many-particle systems on the line with various types of interaction. The relation between the existence of the additional first integrals polynomial in the momenta and differential-functional equations for the unknown potentials is established. We investigate the types of meromorphic interaction potentials admitting additional first integrals, polynomial in the momenta. The exhaustive description of integrable Hamiltonian systems of designated form is obtained.

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