Abstract
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.
Original language | English |
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Pages (from-to) | 239-254 |
Number of pages | 16 |
Journal | Communications in Mathematical Physics |
Volume | 94 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 1984 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics