Dariya Safonova
Kashirskoe sh. 31, Moscow, 115409 Russia
National Research Nuclear University MEPhI
Publications:
Kudryashov N. A., Safonova D. V., Biswas A.
Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation
2019, vol. 24, no. 6, pp. 607614
Abstract
This paper considers the Radhakrishnan – Kundu – Laksmanan (RKL) equation to
analyze dispersive nonlinear waves in polarizationpreserving fibers. The Cauchy problem for
this equation cannot be solved by the inverse scattering transform (IST) and we look for exact
solutions of this equation using the traveling wave reduction. The Painlevé analysis for the
traveling wave reduction of the RKL equation is discussed. A first integral of traveling wave
reduction for the RKL equation is recovered. Using this first integral, we secure a general
solution along with additional conditions on the parameters of the mathematical model. The
final solution is expressed in terms of the Weierstrass elliptic function. Periodic and solitary
wave solutions of the RKL equation in the form of the traveling wave reduction are presented
and illustrated.

Safonova D. V., Demina M. V., Kudryashov N. A.
Stationary Configurations of Point Vortices on a Cylinder
2018, vol. 23, no. 5, pp. 569579
Abstract
In this paper we study the problem of constructing and classifying stationary
equilibria of point vortices on a cylindrical surface. Introducing polynomials with roots at vortex
positions, we derive an ordinary differential equation satisfied by the polynomials. We prove
that this equation can be used to find any stationary configuration. The multivortex systems
containing point vortices with circulation $\Gamma_1$ and $\Gamma_2$ $(\Gamma_2 = \mu\Gamma_1)$ are considered in detail.
All stationary configurations with the number of point vortices less than five are constructed.
Several theorems on existence of polynomial solutions of the ordinary differential equation under
consideration are proved. The values of the parameters of the mathematical model for which
there exists an infinite number of nonequivalent vortex configurations on a cylindrical surface
are found. New point vortex configurations are obtained.
