Symmetries and integrability of differential equations,
method of differential constraints in constructing multi-phase solutions of evolution equations,
equivalence of ordinary differential equations.
Main publications:
Bagderina Yu. Yu., “Invariants of a family of scalar second-order ordinary differential equations for Lie symmetries and first integrals”, Journal Physics A: Math. Theor., 49:15 (2016), 155202
Bagderina Yu. Yu., Tarkhanov N. N., “Solution of the equivalence problem for the third Painlevé equation”, Journal of Mathematical Physics, 56:1 (2015), 013507
Bagderina Yu. Yu., “Linearization criteria for a system of two second-order ordinary differential equations”, Journal Physics A: Math. Theor., 43:46 (2010), 465201
Bagderina Yu. Yu., “Invariants of a family of third-order ordinary differential equations”, Journal Physics A: Math. Theor., 42:8 (2009), 085204
Bagderina Yu. Yu., “Ratsionalnye resheniya evolyutsionnykh uravnenii pyatogo poryadka dlya opisaniya voln na vode”, Prikl. matematika i mekhanika, 72:2 (2008), 288–301