Buslajew received his Ph.D. (Russian candidate degree) in 1963 from the University of Leningrad under Olga Ladyzhenskaya with thesis Short-Wave Asymptotics of Diffraction Problems in Convex Domains. He was a professor at Saint Petersburg State University.
In 1963 he received the prize of the Leningrad Mathematical Society.
In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk Regularization of many particle scattering. He received an honorary doctorate from the Université Paris Nord. In 2000 he received the State Prize of the Russian Federation and he was an Honoured Scientist of the Russian Federation. In 2000 he gave a plenary lecture (Adiabatic perturbations of linear periodic problems) at the annual meeting of the German Mathematical Society in Dresden.
- with Vladimir Borisovich Matveev: "Wave operators for the Schrödinger equation with a slowly decreasing potential". Teoreticheskaya i Matematicheskaya Fizika. 2 (3): 367–376. 1970. Bibcode:1970TMP.....2..266B. doi:10.1007/BF01038047.
- "Semiclassical approximation for equations with periodic coefficients". Russian Mathematical Surveys. 42 (6): 97–125. 1987. Bibcode:1987RuMaS..42...97B. doi:10.1070/RM1987v042n06ABEH001502.
- with Vincenzo Grecchi: "Equivalence of unstable anharmonic oscillators and double wells". Journal of Physics A: Mathematical and General. 26 (20): 5541. 1993. Bibcode:1993JPhA...26.5541B. doi:10.1088/0305-4470/26/20/035.
- with Catherine Sulem: "On asymptotic stability of solitary waves for nonlinear Schrödinger equations". Annales de l'IHP Analyse non linéaire. 20 (3). 2003. Bibcode:2003AnIHP..20..419B. doi:10.1016/S0294-1449(02)00018-5.
- "professors". www.ioffe.ru.
- "Staff — Buslaev Vladimir Savelievich (1937 - 2012)". math.nw.ru.
- Vladimir Savel'evich Buslaev at the Mathematics Genealogy Project
- "On the mathematical work of Vladimir Savel'evich Buslaev". St. Petersburg Mathematical Journal. 25: 151–174. 2014. MR 3114847.
- "L206". www.math.tu-dresden.de.
- Памяти Владимира Савельевича Буслаева (Journal of the Saint Petersburg State University, Number 3847, 14. April 2012)