Framework of extended BKP equations possessing N‐wave solutions in (2+1)‐dimensions.

A universal property in terms of Hirota differential operators is presented, with an aim to construct Hirota bilinear equations possessing Pfaffian formulations in (2+1)‐dimensions. It is then shown that there exist linear combination solutions of exponential waves to various extended Hirota bilinear equations. Applications are made for the (2+1)‐dimensional generalized Hirota–Satsuma–Ito (HSI) equation, the special fourth‐order (2+1)‐dimensional nonlinear equation, and the fifth‐order Korteweg–de Vries (KdV) equation, thereby presenting their particular Pfaffian and multiple wave solutions. [ABSTRACT FROM AUTHOR]