The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via Bell polynomials symbolic computation, bilinear form, Backlund transformation Lax pair for such are obtained. Based on Hirota method, we construct soliton solutions, analyze elastic collisions constant coefficien...

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...

It is known that the governing equations for the evolution of the envelope of weakly nonlinear capillary-gravity wave packets, the so-called Davey-Stewartson equation, admit dromion solutions in the limit of shallow water and strong surface tension, i.e., when kh≪1 and the Bond number (Bo) ≡T/ρgh^{2}>1/3 (where T is the surface tension coefficient and h the water depth). Here we show that capil...

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...

We consider the (coupled) Davey-Stewartson (DS) system and its Bäcklund transformations (BT). Relations among the Davey-Stewartson system, the double KadomtsevPetviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are established. The DS hierarchy and the double KP system are equivalent. The ALH is the BT of the DS system in a certain reduction. From the BT of coupled DS system we can ...

F. T. Smith and K. Stewartson Journal of Fluid Mechanics / Volume 58 / Issue 01 / March 1973, pp 143 ­ 159 DOI: 10.1017/S0022112073002181, Published online: 29 March 2006 Link to this article: http://journals.cambridge.org/abstract_S0022112073002181 How to cite this article: F. T. Smith and K. Stewartson (1973). Plate­injection into a separated supersonic boundary layer. Journal of Fluid Mechan...

The velocity field and the instability of the flow in a rotating square duct were investigated. The velocity profiles were obtained for Ekman numbers less than 1/16 by combining a linear Stewartson layer solution, a non-linear Ekman layer solution and a local similarity assumption. The transition of the secondary-flow pattern from one pair of vortices to two pairs of vortices was studied with t...

The Davey-Stewartson 1(DS1) system[9] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in o...