Chaotic behaviour of the solutions to a perturbed Korteweg-de Vries equation

Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the homoclinic chaos Poincar\'e sections are constructed to demonstrate the complicated behaviour, and Lyapunov exponents are also numerically calculated.