Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized kp (gkp) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. the symmetries of gkp equation with an arbitrary nonlinear term are obtained. the condition that must satisfy for existence the symmetries group of gkp is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. the resulting similarity reductions are studied by performing the bifurcation and the phase portrait of gkp and also the corresponding solitary wave solutions of gkp equation are constructed.