(A) Observation of dispersive shock fronts. Red arrows: signatures of soliton fission. (B) Custom Euler model, including counter-propagation and van der Waals nonlinearities, obtained by evolving a sinusoidal wave initialized with am- plitude H = 0.1h (with computation taking ∼ 4 days on a desktop PC). More details: Supple- mentary Materials, Section 5. (C) KdV solution obtained using Eq. (1).