We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of conformally immersed surfaces is given.

We have once more to record the death of one of the former Presidents of our Society. Dr. J. G. Davey died on February 20th, at the advanced age of 82. He began his professional life as a general practitioner, but circumstances soon transferred him to the special branch of medical work which he continued to the end, viz., the treatment of lunacy and the care of the insane; and it will be seen f...

Up to homeomorphism, there are 9 topologies on a three point set {a, b, c} [4]. Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}. This is an interesting topological space to the extent that every topological space can be embedded in a product of Davey spaces [3]. In this note we will consider the problem of obtaini...

Children with severe developmental delays (three with Down syndrome and three with autism as the primary diagnosis) observed a videotaped model performing two basic dressing skills without prompting, verbal or otherwise, or explanation by an instructor. In a within-subjects design, dressing skills that were presented at a relatively slow presentation speed through videotaped modelling were even...

In this letter, we report the existence of a novel type of explode-decay dromions, which are exponentially localized coherent structures whose amplitude varies with time, through Hirota method for a nonisospectral Davey-Stewartson equation I discussed recently by Jiang. Using suitable transformations, we also point out such solutions also exist for the isospectral Davey-Stewartson I equation it...

Department of Physics, University of Naples Federico II, Napoli, Italy, 2 525 Davey Laboratory, Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA, United States, 3 Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA, United States, 4 104 Davey Laboratory, Department of Physics, Pennsylvania State University, Uni...

Rigorous Melnikov analysis is accomplished for Davey–Stewartson II equation under singular perturbation. Unstable fiber theorem and center-stable manifold theorem are established. The fact that the unperturbed homoclinic orbit, obtained via a Darboux transformation, is a classical solution, leads to the conclusion that only local well posedness is necessary for such a Melnikov analysis. The mai...