ИСТИНА

The study of anomalous waves (rogue waves) in non-linear systems is one of important areas of modern mathematical physics. In particular, the soliton equations are actively used as models for generation of rogue waves. The is a huge literature, dedicated to the applications of 1+1-dimensional soliton systems to the anomalous waves theory, but the 2+1 dimensional case is studied much less. One of the main 2+1 soliton systems, admitting rogue waves type solutions is the focusing Davey-Stewardson 2 equation. In a recent series of papers we constructed asymptotic formulas for spatially-periodic focusing Nonlinear Schrodinger equation under assumption that the Cauchy data is a small perturbation of an unstable background. Such solutions are used as models for generation of rogue waved in non-linear systems. Due to the fact that the spectral curves are close to rational ones, all ingredients of the theta-functional formulas can be explicitly calculated in the leading order. These asymptotic solutions are expressed in terms of elementary functions and provide a good approximation for the exact ones. In the present work we construct analogous formulas for the focusing Davey-Stewardson 2 equation.