Wronskian Formulation and Ansatz Method for Bad Boussinesq Equation

In this work, two variants of the bad Boussinesq equation are studied. A Wronskian formulation is constructed for the solutions of the first equation. Various samples of real and complex solutions are given in accordance with zero and non-zero eigenvalues of the associated linear system of differential equations. Although the Wronskian formulation can also be derived for the second equation, a direct Ansatz method is proposed and successfully applied to obtain real solutions. The method is presented in this paper with concrete examples.