Bound coherent structures propagating on the free surface of deep water

Dmitry Kachulin, Sergey Dremov, Alexander Dyachenko

Research output: Contribution to journalArticlepeer-review


This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko- Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

Original languageEnglish
Article number115
Issue number3
Publication statusPublished - Mar 2021


  • Bi-soliton
  • Breather
  • Dyachenko equations
  • Nonlinear schrödinger equation
  • Soliton
  • Super-compact dyachenko-zakharov equation
  • Surface gravity waves


Dive into the research topics of 'Bound coherent structures propagating on the free surface of deep water'. Together they form a unique fingerprint.

Cite this