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
- 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.
- T. Grava, A. Kapaev and Ch. Klein, On the tritronquee solutions to PI2. Constructive Approximation: vol. 41, Issue 3 (2015), 425-466.
- 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.
- A. A. Kapaev, Quasi-linear Stokes phenomenon for the Painleve first equation. J. Phys. A: Math. Gen., vol.. 37 (2004) 11149-11167.
- 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).
- A. S. Fokas and A. A. Kapaev, Riemann-Hilbert approach to the Laplace equation, J. Math. Anal. Appl., vol. 251 (2000) 770-804.
- A. A. Kapaev, Equations prescribed curvature and deformations of the monodromy group, Physica D, vol. 79 (1994) 87-108.
- A. A. Kapaev, Scaling limits in the second Painleve transcendents, Zap. Nauch. Semin. POMI, vol. 209 (1994) 60-101 (in Russian).
- A. A. Kapaev, Global asymptotics of the second Painleve transcendent, Phys. Lett. A, vol. 167 (1992) 356-362.
- 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:
- Poe dynamics of isomonodromy solutions to the Nonlinear Schroedinger equation.
- Critical asymptotic regimes inthe biorthogonal polynomials.
- Asymptotics of the Heun polynomials in the real case.
Teaching
- Lecture course for graduate students: Riemann-Hilbert problem techniques and Painlevé equations