Multiple Soliton Interactions on the Surface of Deep Water

Dmitry Kachulin, Alexander Dyachenko, Sergey Dremov

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The paper presents the long-Time dynamics with multiple collisions of breathers in the super compact Zakharov equation for unidirectional deep water waves. Solutions in the form of breathers were found numerically by the Petviashvili method. In the terms of envelope and the assumption of the narrow spectral width the super compact equation turns into the well known exact integrable model-nonlinear Schrödinger equation, and the breather solution in this case turns into envelope soliton. The results of numerical simulations show that two main scenarios of long-Time dynamics occur during numerous collisions of breathers. In the first case, one of the breathers regularly takes a number of particles from the other one at each collision and in the second one a structure resembling the bi-soliton solution of nonlinear Schrödinger equation arises during the collision. Despite these scenarios, it is shown that after numerous collisions the only one breather having initially a larger number of particles remains.

Original languageEnglish
Article number65
Issue number2
Publication statusPublished - Jun 2020
Externally publishedYes


  • breather
  • nonlinear Schrödinger equation
  • soliton
  • super compact Zakharov equation
  • surface gravity waves


Dive into the research topics of 'Multiple Soliton Interactions on the Surface of Deep Water'. Together they form a unique fingerprint.

Cite this