ON INTEGRALS OF MOTION OF THE 1-D ZAKHAROV EQUATION

Authors

  • A. I. Dyachenko Landau Institute for Theoretical Physics RAS

DOI:

https://doi.org/10.29006/1564-2291.JOR-2019.47(1).12

Keywords:

water waves, integrals of motion, 1-D Zakharov equation

Abstract

The waves on a free surface of 2D deep water can be split in two groups: the waves moving to the right, and the waves moving to the left. The fundamental consequence of this decomposition is the conservation of the ``number of waves'' in each particular group.

References


  1. Dyachenko A.I., Kachulin D.I., Zakharov V.E. Super compact equation for water waves. Journal of Fluid Mechanic, 2017, Vol. 828, pp. 661–679.

  2. Dyachenko A.I. and Zakharov V.E. Dyachenko A.I. and Zakharov V.E. Is free-surface hydrodynamics an integrable system? Phys. Lett. A, 1994, Vol. 19, pp. 144–14

  3. Dyachenko A.I. and Zakharov V.E. Compact equation for gravity waves on deep water. JETP Letters, 2011, Vol. 93, No. 12, pp. 701–705.

  4. Dyachenko A.I. and Zakharov V.E. A dynamic equation for water waves in one horizontal dimension. European Journal of Mechanics – B/Fluids, 2012, Vol. 32, pp. 17–21.

  5. Zakharov V.E. Stability of periodic waves of finite amplitude on a surface of a depp fluid. Journal of Applied Mechanics and Technical Physics, 1968, Vol. 9, pp. 190–194.

Published

2019-05-28

Issue

Section

The XXII workshop of the Council of nonlinear dynamics of the Russian Academy of

Most read articles by the same author(s)