Nonpropagating soliton and kink soliton in a mildly sloping channel

Abstract

The nonlinear equation governing both the nonpropagating soliton and kink soliton in a channel with slowly varying depth of water has been derived using the perturbation method of multiple scales. Both nonpropagating soliton and kink soliton solutions for the special case of a mildly sloping channel have been given. The effects of the surface tension of water on solitons have been taken into account. The results obtained show that the two types of solitons always move slowly toward the shallow end of the channel with uniform accelerations, and the soliton’s average drift velocities as well as accelerations are proportional to the channel slope and slightly reduced by the surface tension.