Mach Tuck
The wings have an aerodynamic center and that center is at approximately the 25% chord point. However, as the aircraft moves into supersonic flight the up wash ahead of the wing disappears (since no pressure waves move out ahead of the wing.) As a result it is not surprising that the aerodynamic center and center of pressure, both move back to the 50% chord point.
The nose of the aircraft always tends to pitch nose down as the aircraft transitions from subsonic to supersonic speed. This tendency is called the "Mach Tuck." In aircraft such as Concorde the "Fly by Wire" controls compensate for this tendency automatically, so the pilot never notices it. However, if the aircraft was never designed to enter supersonic flight (like most airliners.) the nose would pitch down significantly during the transition through the transonic speed range.
The book you must read is Handling The Big Jets, by Davis, it's tough going but is a must for interview.