The two-singular manifold method: II. Classical Boussinesq system

Abstract

For pt.I see Musette et. al., ibid., vol.24, p.3895 (1994) The two-singular manifold method-a generalization of the singular manifold method of Weiss (1983)-is applied to the classical Boussinesq system, also known as the Broer-Kaup system. From the point of view of its singularity analysis, the important feature of this system is the existence of two principal families with opposite principal parts. The usual singular manifold method takes into account only one of these families at a time. Our generalization takes into account both families, and in this way we are able to derive the Lax pair and Darboux transformation-and hence the auto-Backlund transformation-for the classical Boussinesq system from its Painleve analysis.