Abstract
This paper establishes surprisingly precise a priori bounds on theL ∞-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 parameterc, the phase speed of the waves. These observations do not result from perturbation of linear theory, but are global.
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Communicated by L. Nirenberg
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Toland, J.F. Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves. Commun.Math. Phys. 94, 239–254 (1984). https://doi.org/10.1007/BF01209303
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DOI: https://doi.org/10.1007/BF01209303