General Relativity theory (mathematical methods in black hole physics, theory of gravitational waves, cosmology); theory of nonlinear integrable systems and its applications for investigation of nonlinear properties of strong gravitational fields and their interactions with various types of matter fields.
Main publications:
G. A. Alekseev, “Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations
in the low energy heterotic string effective theory”, Phys. Rev. D, 80 (2009), 041901(R), 4 pp., arXiv: hep-th/0811.1358v1
G. A. Alekseev, “O parametrizatsii dannymi monodromii prostranstv lokalnykh reshenii integriruemykh reduktsii uravnenii Einshteina”, TMF, 143:2 (2005), 278–304; G. A. Alekseev, “Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einsteinfield equations”, Theoret. and Math. Phys., 143:2 (2005), 720–740
G. A. Alekseev, “Gravitational solitons and monodromy transform approach to solution of integrable reductions of Einstein equations”, Physica D, 152 (2001), 97–103, arXiv: gr-qc/0001012
G. A. Alekseev and J. B. Griffiths, “Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves”, Phys. Rev. Lett., 87:22 (2001), 221101, 4 pp., arXiv: gr-qc/0105029
G. A. Alekseev and A. A. Garcia, “Schwarzschild black hole immersed in a homogeneous electromagnetic field”, Phys. Rev. D, 53:4 (1996), 1853–1867
; G. A. Alekseev, “Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einsteinfield equations”, Theoret. and Math. Phys., 143:2 (2005), 
