Leading Researcher, Doctor of Sciences

e-mail: kapaev55@mail.ru

 Directions of research

• integrable systems,
• isomonodromic deformations,
• Riemann-Hilbert problem,
• asymptotic approaches.

Basic Research papers

1. B. Dubrovin and A. Kapaev, On an isomonodromy deformation equation without the Painleve property. Russian J. Math. Phys., vol. 21 (2014) no. 1, pp. 9-35.
2. T. Grava, A. Kapaev and Ch. Klein, On the tritronquee solutions to PI2. Constructive Approximation: vol. 41, Issue 3 (2015), 425-466.
3. A.S. Fokas, A.R. Its, A.A. Kapaev and V.Yu. Novokshenov, Painleve transcendents: the Riemann-Hilbert approach. Math. Surveys and Monographs, vol. 128. Amer. Math. Soc., 2006.
4. A. A. Kapaev, Quasi-linear Stokes phenomenon for the Painleve first equation. J. Phys. A: Math. Gen., vol.. 37 (2004) 11149-11167.
5. A. A. Kapaev, Monodromy approach to the scaling limits in isomonodromy systems. Theor. Math. Phys., vol. 137, no. 3 (2003) 1691-1702. (перевод с: Teoret. i Matemat. Fizika, Том 137 № 3 (2003) 393-407).
6. A. S. Fokas and A. A. Kapaev, Riemann-Hilbert approach to the Laplace equation, J. Math. Anal. Appl., vol. 251 (2000) 770-804.
7. A. A. Kapaev, Equations prescribed curvature and deformations of the monodromy group, Physica D, vol. 79 (1994) 87-108.
8. A. A. Kapaev, Scaling limits in the second Painleve transcendents, Zap. Nauch. Semin. POMI, vol. 209 (1994) 60-101 (in Russian).
9. A. A. Kapaev, Global asymptotics of the second Painleve transcendent, Phys. Lett. A, vol. 167 (1992) 356-362.
10. A. A. Kapaev, Asymptotics of solutions of the Painlevé equation of the first kind. Diff. Eqns., vol. 24 (1989) 1107-1115 (translated from: Differentsial’nye uravnenia, vol. 24 (1988) 1684-1695).

Possible research supervision. Problems:

1. Poe dynamics of isomonodromy solutions to the Nonlinear Schroedinger equation.
2. Critical asymptotic regimes inthe biorthogonal polynomials.
3. Asymptotics of the Heun polynomials in the real case.

Teaching

1. Lecture course for graduate students: Riemann-Hilbert problem techniques and Painlevé equations