arXiv subjects
Publications and source records attributed to V. L. Vereschagin.
The paper concerns asymptotic studies for the sixth Painlevé transcendent as independent variable tends to infinity. The primary tool is averaging and the Whitham method. Elliptic ansatz, appropriate modulation equation and asymptotics for some partial solution to PVI are found.
Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.
The connection between modulated Riemann surface of genus one and solution to Volterra lattice that tends to constants at infinity is studied. The main term of asymptotics for large time of solution to the mentioned Cauchy problem is written out.
Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.
The main subject of the paper is the so-called Discrete Painlevé-1 Equation (DP1). Solutions of DP1 are classified under criterion of their behavior while argument tends to infinity. The Isomonodromic Deformations Method yields asymptotic formulae for regular solutions of DP1. DP1 is an integrable system, what allows to develop appropriate Whitham theory. Asymptotics of singular solutions of DP1 are calculated by using the Whitham method.
The main subject of the paper is the so-called Discrete Painlevé-1 Equation (DP1). Solutions of the DP1 are classified under criterion of their behavior while argument tends to infinity. The appropriate theorems of existence are proved.
The Lie algebra specified by space of local functionals with commutator determined by the Gardner bracket was under survey. Problem of classification of deformations of this bracket over local infinitesimal transformations of functionals was interpreted as a problem of computing the appropriate cohomology group of order 2. The most interesting class of deformations was investigated.