A study on two extensions of the Bogoyavlenskii–Schieff equation

In this work, two extensions of the Bogoyavlenskii–Schieff equation are examined. N-soliton solutions are formally determined for each extended equation. We show that the extension terms do not kill the integrability of the typical Bogoyavlenskii–Schieff equation. The simplified Hirota’s method established by Hereman and Nuseir is applied to achieve this goal.