TY - JOUR

T1 - Multiple Soliton Interactions on the Surface of Deep Water

AU - Kachulin, Dmitry

AU - Dyachenko, Alexander

AU - Dremov, Sergey

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - breather

KW - nonlinear Schrödinger equation

KW - soliton

KW - super compact Zakharov equation

KW - surface gravity waves

KW - COMPACT EQUATION

KW - WAVES

KW - nonlinear Schrodinger equation

KW - COLLISIONS

UR - http://www.scopus.com/inward/record.url?scp=85086030033&partnerID=8YFLogxK

U2 - 10.3390/fluids5020065

DO - 10.3390/fluids5020065

M3 - Article

AN - SCOPUS:85086030033

VL - 5

JO - Experiments in Fluids

JF - Experiments in Fluids

SN - 0723-4864

IS - 2

M1 - 65

ER -