Mixed turbulence of breathers and narrowband irregular waves: mKdV framework
Breathers or oscillating wave packets, along with solitons, are the most energy-carrying waves in various physical media, i.e. surface and internal waves, optical networks, and Josephson junctions. Breathers largely determine the overall wave dynamics of wave fields. In this work, the dynamics of a set of breathers or the so-called breather turbulence or breather gas is studied in the framework of the modified Korteweg–de Vries equation with positive cubic nonlinearity. Different multi-interactions of breathers occurring in a breather gas are analyzed. Numerical simulation of mixed turbulence of breathers and irregular waves is performed. Two approaches are realized: the first corresponds to the comparison of dynamics of the mixed wave fields with a fixed breather component and irregular waves with different momentum. The second corresponds to the comparison of dynamics of the wave fields with the same momentum but with different wave components, including breathers or pure wave fields of irregular waves. The statistical properties of considered wave fields are studied and analyzed. The most extreme wave fields from the point of view of freak waves are identified.