Abstract: This paper discusses a class of classical(2+1)-dimensional KP equation, which has found wide applications in hydrodynamics, plasma physics, gas dynamics. By use of the Painleve analysis, the integrability of nonlinear differential equation is determined. Double linear method of Hirota is a transformation in nature. By testing the form with expanded homoclinic breather limit method, the form of the transformed equation is tested and the rational solution of the nonlinear wave equation is put under examination. Among homoclinic breather solitary waves, the cusp wave solution is worked out when the period of the solitary wave tends to be infinite.