  We propose a novel algorithm, based on physics-informed neural networks
(PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such
as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of
solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the
resulting error. We present several numerical experiments to demonstrate that
PINNs can approximate solutions of these dispersive PDEs very accurately
