Benjamin-Ono Soliton Dynamics in a slowly varying potential revisited

Justin Holmer, Katherine Zhiyuan Zhang

The Benjamin Ono equation with a slowly varying potential is $$\text{(pBO)}{u}_t+(H{u}_x-Vu+\frac{1}{2}{u}^2{)}_x=0$$ with $V(x)=W(hx)$, $0<h\ll 1$, and $W\in C_c^\infty(\mat…