Bell Polynomial Approach and Wronskian Technique to Good Boussinesq Equation

Abstract

The elementary and systematic binary Bell polynomial approach is applied to the good Boussinesq equation. The bilinear representation, $n$-soliton solutions, bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the good Boussinesq equation are obtained directly. In addition, from the reduction conditions of the obtained Lax pairs, the $n$ order $\mathrm{Wronskian}$ determinant solution of the equation is also constructed.