Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

Abstract

We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of ($2+1$)-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized $D_p$-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of $p$ is 5.