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Previous experiments have shown that a bubble detonation wave is a resonant or self-sustained solitary wave in a bubble medium. Bubble detonation is modeled by a solitary wave with energy release in bubbles. The equation describing a solitary wave of small amplitude is shown to be an analog of nonlinear Boussinesq equation of the fourth order. A comparison of the solution obtained with averaged experimental pressure profiles shows that the analytical solution is suitable for describing bubble detonation waves with a finite pressure amplitude. In the model proposed, the time of action of solitary-wave compression on a separate bubble is several times the bubble oscillation period. This result agrees with experimental data and confirms the presence of a collective resonant effect in a bubble medium. Satisfactory agreement is obtained between experimental and theoretical data on the pressure profile and extent and velocity of bubble detonation waves.