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

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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 languageEnglish
Pages (from-to)239-254
Number of pages16
JournalCommunications in Mathematical Physics
Volume94
Issue number2
DOIs
Publication statusPublished - 1 Jun 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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