426034, Izhevsk, 1 Universitetskaya
Laboratory of Nonlinearaty Dynamics and Synergetics
Borisov A. V., Pavlov A. E.
Dynamics and statics of vortices on a plane and a sphere - I
1998, vol. 3, no. 1, pp. 28-38
In the present paper a description of a problem of point vortices on a plane and a sphere in the "internal" variables is discussed. The hamiltonian equations of motion of vortices on a plane are built on the Lie–Poisson algebras, and in the case of vortices on a sphere on the quadratic Jacobi algebras. The last ones are obtained by deformation of the corresponding linear algebras. Some partial solutions of the systems of three and four vortices are considered. Stationary and static vortex configurations are found.
Pavlov A. E., Simakov N. N.
Spatial Chaos of Swift-Howenberg Model
1996, vol. 1, no. 2, pp. 104-110
A Hamiltonian setting of 1-dimensional static Swift-Hohenberg problem which describes a spatial disorder has been introduced. For studying this problem a Painlevé-Kowalevski method based on investigation of meromorphy of general solution is used. In conclusion a stochastic structure of the phase space is demonstrated by means of Poincaré section method.
Pavlov A. E.
The Mixmaster Cosmological Model as a Pseudo-Euclidean Generalized Toda Chain
1996, vol. 1, no. 1, pp. 111-119
The question of the integrability of the mixmaster model of the Universe, presented as a dynamical system with finite degrees of freedom, is investigated in the present paper.