OSCILLATORY SOLITARY WAVES IN A RESONANT SYSTEM BETWEEN LONG GRAVITY AND SHORT CAPILLARY WAVES

Oscillatory solitary waves are analytically examined in a resonant sys tem between long gravity and short capillary waves. Applying the proce dure of the normal form analysis to the interaction equation for stead y state, weakly nonlinear amplitude equations are derived. Solitary wa ve solutions of the equations are shown to be in good agreement with n umerical results in both long and short wave modes, as far as the wave amplitudes are small. Integrability of the interaction system is brie fly discussed in the parameter region where the solutions exist.