Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves

This paper establishes surprisingly precise a priori bounds on the L_∞-norm of certain singular solutions of a system of two nonlinear Sturm-Liouville equations which model solitary water waves. These solutions can be interpreted as homoclinic orbits for a system of four first order ordinary differential equations. The uniqueness of these homoclinic orbits is established for certain choices of a parameter c, the phase speed of the waves. These observations do not result from perturbation of linear theory, but are global.