EXISTENCE OF SOLITARY WAVES FOR WATER-WAVE MODELS

This paper proves the existence of solitary waves for several fifth-or der models for water waves. The method relies on a variational charact erization of these solitary waves. Conclusions include: (1) there are solitary waves with negative speed and small amplitude for fifth-order , Korteweg-de Vries-like models; (2) the minimizing solutions, in the sense of the variational principle considered, are not close to the th ird-order Korteweg-de Vries one-soliton, which may explain difficultie s with the perturbation of the latter solution.