The Bogoyavlenskii-Schiff hierarchy and integrable equations in \((2+1)\) dimensions (Q1573859)

The authors investigate, whether the \((2+1)\)-dimensional Bogoyavlenskii-Schiff equation has its own higher-order integrable equations. The Lax pair for this equation is derived and its integrability in 5th-order is studied. It is shown, that the 5th-order equation admits the Painlevé property. The authors modify the \(L\) and \(T\) operators of the \(p\)-KdV equation for the search of a \((3+1)\)-dimensional integrable equation, but the Lax equation is eventually reduced to a \((2+1)\)-dimensional one.