Wronskian Formulation and Ansatz Method for Bad Boussinesq Equation

Abstract

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.

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Acknowledgments

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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Correspondence to Lu Trong Khiem Nguyen.

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Nguyen, L.T.K. Wronskian Formulation and Ansatz Method for Bad Boussinesq Equation. Vietnam J. Math. 44, 449–462 (2016). https://doi.org/10.1007/s10013-015-0145-z

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Keywords

  • Hirota’s bilinear method
  • Soliton equation
  • Boussinesq equation
  • Wronskian formulation
  • Positon
  • Complexiton
  • Rational solution

PACS

  • 02.30.Ik
  • 02.30.Jr