He was Rudolf Nureyev's roommate during the company's tour to Paris when that dancer defected to the west during which Soloviev also received rave reviews from the French and British dance critics.
Soloviev suffered an Achilles tendon tear while touring in America, and his left leg plie never completely recovered.
Bound by a harsh sense of duty and perfectionist proclivities, Soloviev was never satisfied with his performance, but refused to simplify or retire.
The last new work he was involved with was Leonid Lebedev's The Infanta with Irina Kolpakova, which he performed as a guest artist at the Maly Theater in 1976.
He was the subject of a documentary by Galina Mshanskaya called "I am tired of living in my native land" (1995), shown at Lincoln Center as well as other film festivals in United States which discussed Soloviev's frustrations with being an artist under the Soviet system.