Painlevé properties and exact solutions for the high-dimensional Schwartz Boussinesq equation
Ren Bo(任博)a) and Lin Ji(林机)a)b)†
a Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; b Abdus Salam International Centre for Theoretical Physics, Trieste 34139, Italy
Abstract The usual (1+1)-dimensional Schwartz Boussinesq equation is extended to the (1+1)-dimensional space--time symmetric form and the general (n+1)-dimensional space--time symmetric form. These extensions are Painlevé integrable in the sense that they possess the Painlevé property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space--time symmetric form are obtained by the Painlevé—Bäcklund transformation.
Received: 02 July 2008
Revised: 17 August 2008
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10575087) and the
Natural Science Foundation of Zhejiang Province, China (Grant No
102053).
Cite this article:
Ren Bo(任博) and Lin Ji(林机) Painlevé properties and exact solutions for the high-dimensional Schwartz Boussinesq equation 2009 Chin. Phys. B 18 1161
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