Abundant wave solutions to two novel KP-like equations using an effective integration method

In this work, two new nonlinear evolution equations arising from the B-type Kadomtsev-Petviashvili equation, called BKP-like equations, are investigated. The integration technique that used in this paper to determine the exact solutions of the equation is the generalized exponential rational function method. The examined models may be extended to diversify problems in natural phenomena, such as ocean waves. After applying the aforesaid method, abundant wave solutions are formally generated with some free parameters to exhibit various versions of propagations of traveling solitary waves. Notably, upon choosing appropriate values to free parameters, some kink and periodic waves are demonstrated in 3D figures and 2D contour plots. Most of all, the results show that free parameters drastically influence the existence of all kinds of traveling waves, including nature, profile, and stability. The method used in this paper can be easily adopted in other similar equations in mathematical physics.