  We present a non-chiral version of the Intermediate Long Wave (ILW) equation
that can model nonlinear waves propagating on two opposite edges of a quantum
Hall system, taking into account inter-edge interactions. We obtain exact
soliton solutions governed by the hyperbolic Calogero-Moser-Sutherland (CMS)
model, and we give a Lax pair, a Hirota form, and conservation laws for this
new equation. We also present a periodic non-chiral ILW equation, together with
its soliton solutions governed by the elliptic CMS model.
