Direct and inverse scattering transform analysis of stochastic nonlinear wavefields

The numerical direct and inverse scattering transform applications represent a broad topic of nonlinear wave field studies [1]. Here we investigate various stochastic nonlinear wavefields with the dominant role of a large number of solitons within the one-dimensional nonlinear Schrodinger equation model. First, applying the recently developed direct scattering transform numerical scheme allowing accurate identification of the complete wavefield scattering data [2,3], we find distributions of all soliton parameters (amplitudes, velocities, positions, and phases). Then, using the previously developed numerical tools of solving the inverse scattering problem for a large number of solitons [4], we reconstruct the solitonic content of the initial wave field, which allows us to estimate the role of solitons in the initial wave field composition. Finally, we discuss the obtained scattering data distributions, paying particular attention to the correlations in parameters of different solitons. The presented accurate characterization of soliton positions and phases in stochastic nonlinear wavefields can be used in further studies of such important realms of nonlinear physics as spontaneous modulation instability development [5] and integrable turbulence growing [6].

 

The work was supported by Russian Science Foundation grant No. 20-71-00022.

 

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[3] R. Mullyadzhanov, and A. Gelash, Optics Letters, 44(21), 5298-5301, 2019.

[4] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210, 2018.

[5] D. S. Agafontsev and V. E. Zakharov, Nonlinearity 28, 2791, 2015.

[6] D. S. Agafontsev and V. E. Zakharov, Low Temperature Physics, 46(8), 786-791, 2020.