A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov, “On the nonintegrability of the free surface hydrodynamics”, Pis'ma v Zh. Èksper. Teoret. Fiz., 2013, Volume 98, Issue 1,Pages <nobr>48

This article is cited in 20 papers

NONLINEAR DYNAMICS

On the nonintegrability of the free surface hydrodynamics

A. I. Dyachenko^ab, D. I. Kachulin^b, V. E. Zakharov^abcd

^a Novosibirsk State University
^b Landau Institute for Theoretical Physics, Russian Academy of Sciences
^c University of Arizona, Department of Mathematics
^d P. N. Lebedev Physical Institute, Russian Academy of Sciences

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.

Received: 21.05.2013

Language: English

DOI: 10.7868/S0370274X13130109