arXiv subjects

K. Zheltukhin

Publications and source records attributed to K. Zheltukhin.

3 recordsLinked to original sources

arXiv2000

Recursion Operators of Some Equations of Hydrodynamic Type

We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two higher symmetries and their recursion operators. We also discuss a reduction of $N+1$ systems to $N$ systems of some new equations of hydrodynamic type.

nlin.SI↗

arXiv1999

On the Integrability of a Class of Monge-Ampere Equations

We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampere equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge-Ampere equations. Local as well nonlocal conserved densities are obtained.

hep-th↗

arXiv1999

Some Remarks on Vector-Valued Integration

The article presents a new method of integration of functions with values in Banach spaces. This integral and related notions prove to be a useful tool in the study of Banach space geomtry.

math.FA↗