arXiv subjects

Maxim Ju. Balakhnev

Publications and source records attributed to Maxim Ju. Balakhnev.

2 recordsLinked to original sources

arXiv2008

Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions

A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with $4 \times 4$ matrices are presented.

nlin.SI↗

arXiv2005

Integrable Anisotropic Evolution Equations on a Sphere

V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the n-dimensional sphere. The main result is a complete classification of such equations. Auto-Bäcklund transformations are also found for all equations.

nlin.SI↗