You have a basic supersonic jet, the fuselage will have a rear semi-wing modification that will form a secondary shock wave. Attached on the underside of the fuselage with a horizontal surface that will not have a total length larger than the width of the fuselage, this surface will not be adjustable, as the flow will follow that of the fuselage, and not the wing. The airplane will not be taking off at supersonic speeds, and using an altitude-speed relationship, that the 2 shockwaves will meet above ground (in the air somewhere), and not totally cancel each other out, but the primary shock wave would be broken up, and hopefully weaken enough so that when it does reach ground, it will be harmless.

A second approach has the rear semi-wing to have a trailing edge that is adjustable with the aerilons on the wing, the length from attachment to the horizontal edge is larger than the fuselage so that the secondary shock wave would be adjusted according to speed and altitude.