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A second Wronskian formulation of the Boussinesq equation. (English) Zbl 1159.37425
Summary: A Wronskian formulation leading to rational solutions is presented for the Boussinesq equation. It involves third-order linear partial differential equations, whose representative systems are systematically solved. The resulting solutions formulas provide a direct but powerful approach for constructing rational solutions, positon solutions and complexiton solutions to the Boussinesq equation. Various examples of exact solutions of those three kinds are computed. The newly presented Wronskian formulation is different from the one previously presented by Ch.-X. Li et al. [Inverse Probl. 23, No. 1, 279–296 (2007; Zbl 1111.35044)], which does not yield rational solutions.
##### MSC:
 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 35Q58 Other completely integrable PDE (MSC2000) 35Q51 Soliton-like equations