1. Asymptotic methods for the solution of linear and nonlinear equations of mathematical physics.
2. Semiclassical quantization of nonintegrable Hamiltonian systems.
3. Asymptotic methods for financial mathematics.
4. Reaction-diffusion equations.
Main publications:
Lisok A.L., Shapovalov A.V. and Trifonov A.Yu., “Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation”, Sym., Integ. and Geom.: Meth. and Appl., 9 (2013), 066, 1–21
Belov V.V., Litvinets F.N. and Trifonov A Yu., “The semiclassical spectral series for a Hartree-type equation corresponding to a rest point of the Hamilton–Ehrenfest system”, Theor. Math. Phys., 150:1 (2007), 26–40
Belov V.V., Trifonov A.Yu. and Shapovalov A.V., “The trajectory-coherent approximation and the system of moments for the Hartree type equation”, Int. J. of Math. and Math. Scien., 32:6 (2002), 325–370
Bagrov V.G., Belov V.V., Trifonov A.Yu., “Semiclassical trajectory-coherent approximation in quantum mechanics: I. High order corrections to multidimensional time-dependent equations of Schrodinger type”, Ann. of Phys. (N.Y.), 246:2 (1996), 231–290
Bagrov V.G., Belov V.V., Yevseyevich A.A., Trifonov A.Yu., “Quasiclassical spectral series of the Dirac operators corresponding to quantized two-dimensional Lagrangian tori”, J. Phys. A: Math. Gen., 27:15 (1994), 5273–5306
