Khruslov’s scientific interests focus on mathematical physics. He was one of the founders of the theory of averaging of differential operators with particle derivatives. Khruslov proved the theorem of step-type initial data decay for Korteweg-de Vries equation for an infinite series of asymptotic solitons. This way he was the first to obtain the exact formula for the leading term of the asymptotic solution, including the values of all the constants comprising it.

Some of his studies explore the theory of inverse problems of electromagnetic probing. Khruslov’s methods are not only theoretically significant, but also prove to be effective when processing data of real geophysical experiments.

Khruslov is the author of more than 120 scientific works and three monographs.

Titles

Head of Academic Board of Mathematical Department and Thesis Committee of Institute for Low Temperature Physics and Engineering (ILTPE), member of Editorial Boards of two international journals and ILTPE, member of Bureau of Mathematics Department of National Academy of Sciences of Ukraine.

Awards

Laureate of State Prize of Ukraine in Science and Technology (1989), M. Krylov Prize of National Academy of Science of Ukraine (1996) and M. Lavrentiev Prize (2007), Order of Badge of Honor (1985), Order of Merit, Class III (2008), Certificate of Merit of Verkhovna Rada of Ukraine (2010).