Wronskian Formulation and Ansatz Method for Bad Boussinesq Equation
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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.
KeywordsHirota’s bilinear method Soliton equation Boussinesq equation Wronskian formulation Positon Complexiton Rational solution
The author thanks the anonymous referees whose comments and suggestions improved the clarity of presentation and the scientific aspect of the paper.
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