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Solutions of the Classical Boussinesq Equation and the Spherical Boussinesq Equation: The Wronskian Technique

1986; Physical Society of Japan; Volume: 55; Issue: 7 Linguagem: Inglês

10.1143/jpsj.55.2137

1347-4073

Ryogo Hirota,

Advanced Differential Equations and Dynamical Systems

The rational solutions to the classical Boussinesq equation conjectured by Nakamura and the author are proved to be true by the use of the Wronskian technique developed by Freeman and Nimmo. It is also found that a non-auto Bäcklund transformation between a rational solution of the spherical Boussinesq equation with a time-dependent velocity term is nothing but the similarity form of the classical Boussinesq equation.