Lie algebras and equations of Korteweg-de Vries type
- V. Drinfel'd, V. Sokolov
- Mathematics
- 1 July 1985
The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and…
The Symmetry Approach to Classification of Integrable Equations
- A. Mikhailov, A. Shabat, V. Sokolov
- Mathematics
- 1991
In this volume each of the contributors proposes his own test to recognize integrable PDEs. We believe that, independently from the basic definition of integrability, the test must satisfy some…
Integrable Evolution Equations on Associative Algebras
- P. Olver, V. Sokolov
- Mathematics
- 1 April 1998
Abstract:This paper surveys the classification of integrable evolution equations whose field variables take values in an associative algebra, which includes matrix, Clifford, and group algebra valued…
Exactly integrable hyperbolic equations of Liouville type
- A. V. Zhiber, V. Sokolov
- Mathematics
- 28 February 2001
This is a survey of the authors' results concerning non-linear hyperbolic equations of Liouville type. The definition is based on the condition that the chain of Laplace invariants of the linearized…
On construction of recursion operators from Lax representation
- M. Gurses, A. Karasu, V. Sokolov
- Mathematics, Computer Science
- 6 September 1999
In this work, a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation is developed and the recursions operators for some KdV-type systems of integrability equations are found.
Vector-matrix generalizations of classical integrable equations
- S. I. Svinolupov, V. Sokolov
- Mathematics
- 1 August 1994
Some vector-matrix generalizations, both known and new, for well-known integrable equations are presented. All of them possess higher symmetries and conservation laws.
Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
- V. Sokolov, A. Tsiganov
- Mathematics
- 1 April 2002
We consider a quadratic deformation of the Kowalevski top. This deformation includes a new integrable case for the Kirchhoff equations recently found by one of the authors as a degeneration. A 5×5…
Integrable pseudopotentials related to generalized hypergeometric functions
- A. Odesskii, V. Sokolov
- Mathematics, Physics
- 1 March 2008
We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2 + 1)-dimensional…
Integrable (2+1)-dimensional systems of hydrodynamic type
- A. Odesskii, V. Sokolov
- Mathematics
- 9 June 2010
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The Gibbons-Tsarev (GT) systems are most…
Poisson maps and integrable deformations of the Kowalevski top
- I. Komarov, V. Sokolov, A. Tsiganov
- Mathematics
- 16 April 2003
We construct a Poisson map between manifolds with linear Poisson brackets corresponding to the Lie algebras e(3) and so(4). Using this map we establish a connection between the deformed Kowalevski…
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