Multiple Soliton Interactions on the Surface of Deep Water

Abstract

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.

Bound Coherent Structures Propagating on the Free Surface of Deep Water

“…It was observed for the first time in [25] that a collision of two single breathers with very close velocities could result in the formation of a periodically oscillating structure resembling the NLSE bi-soliton. Therefore, the obvious step to obtain the bound structure is to take two single breathers and then set them at the same point in space as initial conditions.…”

“…It should be noted that, so far, in the SCDZE, only stable solutions in the form of a single breather are known. However, an unexpected result was obtained in [25], where multiple collisions of breathers in the periodic domain were studied. It was shown that the only one coherent structure remained at the end regardless of the breathers number and initial parameters.…”

Chaotic Dynamics of the Interface between Dielectric Liquids at the Regime of Stabilized Kelvin-Helmholtz Instability by a Tangential Electric Field

“…The nonlinear Schrödinger (NLS) and Korteweg de Vries (KdV) equations are the classic examples of equations that admits solitary wave solutions [16,17]. The NLS equation originally arises in describing the propagation of narrow spectral wave packets on the fluid boundary in a gravitational field [16] (the soliton dynamics is studied in the recent works [18][19][20]). The KdV equation describes nonlinear waves in the long-wave region of the spectrum, that is, where the length of surface perturbations is significantly greater than the depth of the fluid [17].…”

Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework

“…Three soliton collisions in warm magnetized plasmas were investigated in [13]. An increase in the number of interacting particles leads to rarefied and dense soliton gases [14][15][16][17][18][19][20][21][22][23][24][25]. An ensemble of interacting solitons can appear from the evolution of some initial conditions or as a result of modulation instability driven by random perturbations of an unstable plane wave.…”