In this paper, we study the regularity properties of solutions to Davey–Stewartson system. It is shown that for initial data in a Sobolev space, nonlinear part solution flow resides smoother space than all times. We also obtain norm evolution grows at most polynomially. As an application smoothing estimate, long-term dynamics forced and weakly damped regard, give new proof existence smoothness ...

Abstract In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in Stratonovich sense are discussed. We use two different approaches, namely Riccati-Bernoulli sub-ordinary differential and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, rational solutions. Due significance of theory turbulence for ...

We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with gauge invariant power-law nonlinearities and non-local perturbations. The model includes the Davey–Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variant. Our analysis reveals a new localization phenomenon for non-local perturbations in the high freq...