Chaotic analysis of weakly damped parametrically excited cross-waves with surface tension (Q1777502)

This lengthy paper applies an extension of the generalized Melnikov method to non-autonomous systems that support weakly damped parametrically excited cross-waves in a long rectangular channel when surface tension is present. The purpose is to demonstrate that cross-waves are chaotic by examining the mathematical structure that is involved. The system of non-autonomous evolution equations derived from Hamilton's equations of motion of the second kind is averaged to enable an autonomous system to be analyzed. The chaotic motion for the perturbed dissipative system with surface tension is demonstrated by numerical computation of positive Lyapunov characteristic exponents.