On the highly recommended "Destination: Out" blog, trumpeter Dave Douglas writes about his vision on solo trumpet performances, and he gives a list of recommended listening. I only give his intro and recommend you click on the link below to listen to his suggestions.
"It’s an unusual breed, the solo trumpet recording. Surprisingly, the music is not really for specialists (not that there are many specialists anyway). More to the point, so much of the music goes beyond specifically instrumental interests. Though it is extremely demanding physically, the challenge is really compositional.
The demands are akin to an event like the Iron Man, a 2-mile swim, 120-mile bike, 26-mile run. It requires lots of different skills, enormous reserves of stamina, and a basic belief in one’s ability to pull it off. Preparation is never-ending. Persistence is indispensable, as well as a compulsive desire to see it through. It’s a commitment.
In addition, it requires a point of view. After all that’s been done with these instruments, solo pieces can’t be achieved with chops alone. Solo trumpeting is different from solo piano, for example, because all you’ve got is a metal tube, air, and three valves. Any counterpoint has to be an illusion. It takes a lot of ingenuity to create harmony from a single line. All of the tracks here attack these problems in one way or another.
There is one advantage to the trumpet: because a vibrating lip creates the main body of sound, there is infinite variety to the timbral and textural resources. Though two people may play the same horn, no two people have the same lip. That’s what makes each of these tracks come alive with the creator’s intention."
For the full topic, and Dave Douglas's recommendations : see Destination: Out
Mark O'Keeffe - Knight Errant - Solo Music For Trumpet (2007)
Rex Richardson - Masks - Etudes for solo trumpet
Samuel Adler - Cantos for Solo Instruments (David Bilger, tp) (1998)
Gerard Schwarz - Performs New Music For Trumpet (1990)
Hans Erich Apostel - Sonatina for trumpet solo, Op 42a
Takemitsu Toru - Paths
Stefan Wolpe - Solo Piece for trumpet
Hanz Werner Henze - Sonatina For Solo Trumpet (1974)
Hakan Hardenberger - Exposed Throat
Hakan Hardanberger - Emotion
Choi Sun Bae - Freedom solo trumpet improvisations (1998)