On the interaction between two nonpropagating hydrodynamic solitons

Abstract

The evolution equation governing the positions of two interacting nonpropagating solitons is found by using the variational principle approach. Furthermore, the potential which characterizes the interaction between solitons is derived, from which some important results are obtained: (1) Two solitons with the same polarity always attract each other, while those with opposite polarity repel. (2) The repulsion is much weaker than the attraction and both attraction and repulsion are of short distance. (3) The period of mutual oscillation caused by interaction between two solitons with the same polarity increases as the drive amplitude rises; especially, the period can spread from zero to infinity as the initial distance between solitons increases. All the above results are well coincident with experiments.