Эффект отрицательной скорости частиц в солитонном газе в рамках уравнений типа Кортевега — де Вриза

Вестник Московского университета. Серия 3: Физика и астрономия. 2017. № 5. С. 10–16.

Pelinovsky E., Didenkulova E.

The effect of changing the direction of motion of a defect (a soliton of small amplitude) in soliton
lattices described by the Korteweg–de Vries and modified Korteweg–de Vries integrable equations (KdV and
mKdV) was studied. Manifestation of this effect is possible as a result of the negative phase shift of a small
soliton at the moment of nonlinear interaction with large solitons, as noted in [1], within the KdV equation.
In the recent paper [2], an expression for the mean soliton velocity in a “cold” KdV-soliton gas has been
found using kinetic theory, from which this effect also follows, but this fact has not been mentioned. In the
present paper, we will show that the criterion of negative velocity is the same for both the KdV and mKdV
equations and it can be obtained using simple kinematic considerations without applying kinetic theory. The
averaged dynamics of the “smallest” soliton (defect) in a soliton gas consisting of solitons with random amplitudes
has been investigated and the average criterion of changing the sign of the velocity has been derived and
confirmed by numerical solutions of the KdV and mKdV equations.

Keywords: солитон, уравнение Кортевега-де Вриза, модифицированное уравнение Кортевега - де Вриза