Uniqueness and a priori bounds for certain homoclinic orbits of a Boussinesq system modelling solitary water waves |
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Authors: | J F Toland |
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Institution: | (1) School of Mathematics, University of Bath, BA2 7AY Claverton Down, Bath, England |
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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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