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

Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems