Solitons in dissipative systems subjected to random force within the Benjamin–Ono type equation

Chaos, Solitons and Fractals. 2024. Vol. 187. Article 115373.

Flamarion M., Pelinovsky E.

Solitary wave dynamics is investigated under the assumption of small dissipation and an external random force.
Through a change of variables, the problem becomes homogeneous, allowing for the derivation of asymptotic
algebraic soliton solutions. This change of variables makes the randomness manifest primarily on the soliton
phases. Consequently, the averaged soliton field and the statistical moments can be computed analytically,
assuming that the phase follows a uniform distribution. In the absence of Reynolds dissipation, we show that
the soliton-averaged field tends to spread and dampen as the dispersion increases. In addition, in the presence
of Reynolds dissipation, we demonstrate that algebraic solitons can transition between thick and thin soliton
states. Moreover, when there is viscosity in the upper moving layer, the averaged soliton field exhibits a
dynamic evolution from soliton to thick soliton to soliton, contingent upon the parameter settings

Keywords: солитоны, solitons