Abstract
This paper studies the Kadomtsev-Petviashvili equation of B-type that appears in Fermion fields. The travelling wave hypothesis will be first employed to obtain its solitary wave solution. The constraint condition will also be revealed, in this context. Subsequently, the extended F-expansion method will be applied to this equation to obtain several other solutions to this equation. These will include cnoidal and snoidal wave solutions and their respective limiting cases. The Lie symmetry analysis is carried out to obtain several other solutions.