On the nonintegrability of the free surface hydrodynamics
A. I. Dyachenko+*, D. I. Kachulin*, V. E. Zakharov+*×°
+Novosibirsk State University, 630090 Novosibirsk, Russia
*Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia
×Department of Mathematics, University of Arizona, AZ 857201 Tucson, USA
°Lebedev Physical Institute of RAS, 119991 Moscow, Russia
Abstract
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.