CAPILLARY-GRAVITY SOLITARY WAVES WITH DAMPED OSCILLATIONS

Capillary-gravity solitary waves with damped oscillations are studied analytically. The analysis follows the work of Iooss and Kirchgassner who proved that these waves exist for all values of the Froude number smaller than one. The water-wave problem is reduced to a system of ordinary differential equations by using the center manifold theorem. The normal form of this reduced system can be obtained and a good approximation to these waves for small amplitude is constructed. The limit as the water depth becomes infinite is considered as a special case. A comparison with existing numerical results is made for small-amplitude waves.