  Strongly nonlinear models of internal wave propagation for incompressible
stratified Euler fluids are investigated numerically and analytically to
determine the evolution of a class of initial conditions of interest in
laboratory experiments. This class of step-like initial data severely tests the
robustness of the models beyond their strict long-wave asymptotic validity, and
model fidelity is assessed by direct numerical simulations (DNS) of the parent
Euler system.
  It is found that the primary dynamics of near-solitary wave formation is
remarkably well predicted by the models for both wave and fluid properties, at
a fraction of the computational costs of the DNS code.
