Periodic traveling--wave solutions of nonlinear dispersive evolution equations

For a general class of nonlinear, dispersive wave equations, existence of periodic, traveling-wave solutions is studied. These travelingwaveforms are the analog of the classical cnoidal-wave solutions of the Korteweg-de Vriesequation. They are determined to bestable to perturbation of the same period. Their large wavelengthlimit is shown to be solitary waves.