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2013
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# 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.  607-614 Abstract This paper considers the Radhakrishnan – Kundu – Laksmanan (RKL) equation to analyze dispersive nonlinear waves in polarization-preserving 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. Keywords: Radhakrishnan – Kundu – Laksmanan equation, integrability, traveling waves, general solution, exact solution Citation: Kudryashov N. A., Safonova D. V., Biswas A.,  Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation, Regular and Chaotic Dynamics, 2019, vol. 24, no. 6, pp. 607-614 DOI:10.1134/S1560354719060029
 Safonova D. V., Demina M. V., Kudryashov N. A. Stationary Configurations of Point Vortices on a Cylinder 2018, vol. 23, no. 5, pp.  569-579 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. Keywords: point vortices, stagnation points, stationary configuration, vortices on a cylinder, polynomial solution of differential equation Citation: Safonova D. V., Demina M. V., Kudryashov N. A.,  Stationary Configurations of Point Vortices on a Cylinder, Regular and Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 569-579 DOI:10.1134/S1560354718050064