In this note we show that for certain choice of parameters the hyperbolic–elliptic–elliptic generalized Davey–Stewartson system admits time-dependent travelling wave solutions of the kind given in [V.A. Arkadiev, A.K. Pogrebkov, M.C. Polivanov, Inverse scattering transform method and soliton solutions for Davey–Stewartson II equation, Physica D 36 (1989) 189–197] for the hyperbolic Davey–Stewar...

The linearized Davey-Stewartson equation with varing coefficients is solved by Fourier method. The approach uses the inverse scattering transform for the Davey-Stewartson equation.

The Bäcklund-Darboux transformations are successfully utilized to construct heteroclinic orbits of Davey-Stewartson II equations through an elegant iteration of the transformations. In [17], we successfully built Melnikov vectors with the gradients of Floquet discriminants. Since there is no Floquet discriminant for Davey-Stewartson equations (in contrast to nonlinear Schrödinger equations [17]...

1. Davey Smith G, Ebrahim S. ‘Mendelian randomization’: can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol 2003;32:1–22. 2. Burgess S, Timpson NJ, Ebrahim S, Davey Smith G. Mendelian randomization: where are we now and where are we going? Int J Epidemiol 2015;44:379–88. 3. Haycock PC, Burgess S, Wade KH, Bowden J, Relton C, Davey Smith G....

The Davey-Stewartson equations are used to describe the long time evolution of a threedimensional packets of surface waves. Assuming that the argument functions are quadratic in spacial variables, we find in this paper various exact solutions modulo the most known symmetry transformations for the Davey-Stewartson equations.

Brian H. Feighner, Stephen Eubank, Robert J. Glass, Victoria J. Davey, Jean-Paul Chrétien, and Joel C. Gaydos Author affiliations: The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA (B.H. Feighner); Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA (S. Eubank); Sandia National Laboratories, Albuquerque, New Mexico, USA (R.J. Glass); US De...