4 papers
Vector systems of Painlevé type
V. E. Adler, V. V. Sokolov
The group reduction procedure is applied to vector generalizations of the NLS, mKdV, and KdV equations. The resulting ODE systems admit isomonodromic Lax representations and are mu…
On vector Schwarz-KdV equation
M. Balakhev, V. Sokolov
A collection of miscellaneous continuous, semi-discrete, and discrete integrable systems can be associated with each integrable evolution equation of the KdV type. We give them for…
Novikov equations for commuting differential operators of orders 3,4,5
G. B. Shabat, V. V. Sokolov, A. V. Tsiganov
We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method…
Integrability conditions for Boussinesq type systems
Rafael Hernandez Heredero, Vladimir Sokolov
The symmetry approach to the classification of evolution integrable partial differential equations (see, for example \cite{MikShaSok91}) produces an infinite series of functions, d…