A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory (Q1302137)

The authors prove an existence result for solitary wave solutions to the classical water wave problem. The hydrodynamic problem depends on two-dimensional parameters \(\alpha= gh/c^2\) and \(\beta= \sigma/\rho hc^2\), where \(g,\sigma,h,c,\rho\) denote, respectively, the acceleration due to gravity, the coefficient of surface tension, the asymptotic depth of water, the velocity of solitary wave, and the fluid density. The main result concerns the existence of infinitely many geometrically distinct modulated solitary wave solutions for certain values of the above parameters.