The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
We investigate the sequence of Boussinesq equations by the method of singular manifolds. For the Boussinesq equation, which is known to possess the Painlevé property, a Bäcklund transformation is defined. This Bäcklund transformation, which is formulated in terms of the Schwarzian derivative, obtains the system of modified Boussinesq equations and …