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Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 449–462 | Cite as

Wronskian Formulation and Ansatz Method for Bad Boussinesq Equation

  • Lu Trong Khiem NguyenEmail author
Article

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.

Keywords

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

PACS

02.30.Ik 02.30.Jr 

Notes

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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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Ruhr-Universität BochumBochumGermany
  2. 2.Lehrstuhl für Mechanik - MaterialtheorieRuhr-Universität BochumBochumGermany

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