Benjamin-Ono soliton dynamics in a slowly varying potential

摘要

The Benjamin Ono equation with a slowly varying potential is with , , and , and H denotes the Hilbert transform. The soliton profile is Q(a,c)(x) = cQ(c(x - a)), where and , c > 0 are parameters. For initial condition u(0)(x) to (pBO) close in to Q(0,1)(x), we show that the solution to (pBO) remains close in to Q(a(t),c(t))(x) and specify the parameter dynamics on an O(h(-1)) time scale.