2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95439We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability of a Kirchhoff vortex and a point vortex by the variable separation method is qualitatively analyzed. A new case of integrability of two Kirchhoff vortices is found. A reduced form of equations for two Kirchhoff vortices is proposed and used to analyze their regular and chaotic behavior.27 pages, 7 figuresExactly Solvable and Integrable Systemstext