On the nonintegrability of the free surface hydrodynamics

We study integrability of the compact 1-D Zakharov equation. The results of numerical experiments on multiple collisions of breathers (which correspond to envelope solitons in the NLSE approximation) show that collisions are not pure elastic. Also we analyse the amplitude of six-wave interactions for compact 1-D Zakharov equation. It was found that six-wave amplitude is not canceled for this equation. Thus, 1-D Zakharov equation is not integrable.