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 ...

We prove that the Davey-Stewartson approximation (which degenerates into a cubic Schrödinger equation in 1D) furnishes a good approximation for the exact solution of a wide class of quadratic hyperbolic systems. This approximation remains valid for large times of logarithmic order. We also consider the general case where the polarized component of the mean field needs not to be well-prepared. T...

In this letter, taking the well known (2+1)-dimensional soliton systems, Davey-Stewartson (DS) model and the asymmetric Nizhnik-Novikov-Veselov (ANNV) model, as two special examples, we show that some types of lower dimensional chaotic behaviors may be found in higher dimensional soliton systems. Especially, we derive two famous chaotic system described by ordinary differential equation (ODE) s...

Bäcklund transformations, which are relations among solutions of partial differential equations–usually nonlinear–have been found and applied mainly for systems with two independent variables. A few are known for equations like the Kadomtsev-Petviashvili equation [1], which has three independent variables, but they are rare. Wahlquist and Estabrook [2] discovered a systematic method for searchi...

In this letter, taking the well known (2+1)-dimensional soliton systems, Davey-Stewartson (DS) model and the asymmetric Nizhnik-Novikov-Veselov (ANNV) model, as two special examples, we show that some types of lower dimensional chaotic behaviors may be found in higher dimensional soliton systems. Especially, we derive the famous Lorenz system and its general form from the DS equation and the AN...

Abstract By introducing and solving a new cross-constrained variational problem, one-to-one correspondence from the prescribed mass to frequency of soliton is established for generalized Davey-Stewartson system in two-dimensional space. Orbital stability small soiltons depending on frequencies proved. Multisolitons with different speeds are constructed by stable solitons.

In this paper, we provide a class of surfaces called ϵ-isothermic surface in the pseudo-Euclidean 3-space and introduce pseudo-Calapso equation. We prove that for each surface, can associate two solutions to particular, Calapso, Zoomeron Davey-Stewartson III equations. sequence, classify Dupin having distinct principal curvatures explicit coordinates such surfaces. As application theory, obtain...