2019
Том 71
№ 11

Pritula N. N.

Articles: 9
Brief Communications (English)

Differential-geometric structure and the Lax – Sato integrability of a class of dispersionless heavenly type equations

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 293-297

This short communication is devoted to the study of differential-geometric structure and the Lax – Sato integrability of the reduced Shabat-type, Hirota, and Kupershmidt heavenly equations.

Chronicles (Ukrainian)

The fifteenth scientific session of mathematical commission of the Shevchenko Scientific Society

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1584

Article (Ukrainian)

Finite-Dimensional Nonlocal Reductions of the Inverse Korteweg–de Vries Dynamical System

Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 160-168

We study finite-dimensional Moser-type reductions for the inverse nonlinear Korteweg–de Vries dynamical system and the Liouville integrability of these reductions in quadratures.

Article (Ukrainian)

Lie-algebraic structure of integrable nonlinear dynamical systems on extended functional manifolds

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1512–1518

We consider the general Lie-algebraic scheme of construction of integrable nonlinear dynamical systems on extended functional manifolds. We obtain an explicit expression for consistent Poisson structures and write explicitly nonlinear equations generated by the spectrum of a periodic problem for an operator of Lax-type representation.

Article (Ukrainian)

Nonlinear integrable systems related to the elliptic lie—baxter algebra

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 220-235

We construct a hierarchy of Poisson Hamiltonian structures related to an “elliptic” spectral problem and determine the generating operators for the equation of asymmetric chiral 0 (3) — field.

Brief Communications (Ukrainian)

Structure of integrable supersymmetric nonlinear dynamical systems on reduced invariant submanifolds

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1292–1295

Based on an analysis of a supersymmetric extension of the algebra of pseudodifferential operators on $ℝ^1$ an infinite hierarchy of supersymmetric Lax-integrable nonlinear dynamical systems is constructed by means of the Yang-Baxter $ℛ$-equation method. The structure of these systems on reduced invariant submanifolds specified by a natural invariant Lax-type spectral problem is investigated.

Article (Ukrainian)

The complete integrability analysis of the inverse Korteweg-de Vries equation

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1239–1248

Article (Ukrainian)

Analysis of integrability of the generalized Kadomtsev-Petviashvili type model

Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 800–806

Article (Ukrainian)

Quantum lie algebra of currents ? The universal algebraic structure of symmetries of completely integrable dynamical systems

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 764–768