Abstract
Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as deep water, shallow water waves, internal waves in the stratified ocean, and optical fibers. We study the features of different regimes of collisions between a soliton and a breather in the framework of the focusing modified Korteweg–de Vries equation, where cubic nonlinearity is essential. The relative phase of these structures is an important parameter determining the dynamics of soliton–breather collisions. Two series of experiments with different values of the breather’s and soliton’s relative phases were conducted. The waves’ amplitudes resulting from the interaction of coherent structures depending on their relative phase at the moment of collision were analyzed. Wave field moments, which play a decisive role in the statistics of soliton gases, were determined.
Highlights
Solitons and breathers are a part of different wave systems’ dynamics, primarily hydrodynamics and optics [1,2]
Analysis of two soliton interactions as an elementary act of soliton turbulence has shown the key role of such processes in rarefield soliton gas statistics within the KdV-like models: [4]—within the
It is shown that an important parameter that determines the dynamics of collisions q) were conducted
Summary
Solitons and breathers are a part of different wave systems’ dynamics, primarily hydrodynamics and optics [1,2] Analytical solutions of solitons and breathers optimal focusing into rogue wave were obtained in [31,32] for mKdV and Gardner equation. While the quadratic nonlinearity is much smaller than the cubic one, the Gardner equation can be reduced to the modified KdV equation with the exact soliton and breather solutions [39,40]. We conduct a series of numerical experiments of the interaction between a soliton and a breather in the framework of the modified Korteweg–de Vries equation for different initial wave phases.
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