This paper considers the feasibility of creating dispersion-free solitary quantum-mechanical wave packets. The analysis is carried out within a general framework of quantum-optimal control theory. A key to the realization of solitary quantum wave packets is the ability to create traveling wave potentials U(x - nu t) with coordinated space and time dependence where nu is a characteristic speed. As an illustration, the case of an atom translating in a designed optical trap is considered. Three examples are treated within this framework: (A) the motion of a dispersion-free traveling bound state, (B) feedback-stabilized solitonic motion, and (C) feedback-stabilized solitonic motion in the presence of auxiliary physical objectives. The quantum solitons of (B) and (C) satisfy a nonlinear Schrodinger-type equation with laboratory feedback in the form of an observation of the probability density. This feedback is essential for maintaining the solitonic-type motion. Some generalizations and potential applications of these concepts are also discussed.