Interaction of solitons with long waves in a rotating fluid

Interaction of a soliton with long background waves is studied within the framework of rotation modified Korteweg-de Vries (rKdV) equation. Using the asymptotic method for solitons propagating in the field of a long background wave we derive a set of ODEs describing soliton amplitude and phase with respect to the background wave. The shape of the background wave may range from a sinusoid to the limiting profile representing a periodic sequence of parabolic arcs. We analyse energy exchange between a soliton and the long wave taking radiation losses into account. It is shown that the losses can be compensated by energy pumping from the long wave and, as the result, a stationary soliton can exist, unlike the case when there is no variable background. A more complex case when a free long wave attenuates due to the energy consumption by a soliton is also considered. Some of the analytical results are compared with the results of direct numerical calculations within the framework of the rKdV equation. (C) 2016 Elsevier B.V. All rights reserved.