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.
Highlights
Turbulence in nonlinear continuous media often accompanied by the appearance of localized nonlinear structures
In work [17], the dynamics of one pairwise breather collision were studied in details, and the results were compared with well-known dynamics of the nonlinear Schrödinger equation (NLSE) solitons pairwise interaction
We studied long-time dynamics in the super-compact Zakharov equation (SCZE) for unidirectional deep water waves
Summary
Turbulence in nonlinear continuous media often accompanied by the appearance of localized nonlinear structures. The nonlinear Schrödinger equation (NLSE) is a special case of such models and a universal model for wave turbulence studying. The results of numerical experiments show that the radiation of incoherent waves is small and it is clearly observed that the phases of breathers are synchronized at the moment of collision [17,18]. This allows us, in a sense, to consider the SCZE very similar to the NLSE or NLSE-like and call it “almost integrable”. We can expect that numerous breathers interactions in the SCZE model will result in the formation of a single breather
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