  We study various properties of the soliton solutions of the modified
regularized long-wave equation. This model possesses exact one- and two-soliton
solutions but no other solutions are known. We show that numerical
three-soliton configurations, for which the initial conditions were taken in
the form of a linear superposition of three single-soliton solutions, evolve in
time as three-soliton solutions of the model and in their scatterings each
individual soliton experiences a total phase-shift that is the sum of pairwise
phase-shifts. We also investigate the soliton resolution conjecture for this
equation, and find that individual soliton-like lumps initially evolve very
much like lumps for integrable models but eventually (at least) some blow-up,
suggesting basic instability of the model.
