  The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions.
However, it is not known yet whether it has N-soliton solutions for any N.
Viewing it as a perturbed KdV equation, the asymptotic expansion of the
solution is developed through third order within the framework of a Normal Form
analysis. It is shown that the equation is asymptotically integrable through
the order considered. Focusing on the soliton sector, it is shown that the
higher-order corrections in the Normal Form expansion represent purely
inelastic KdV-soliton-collision processes, and vanish identically in the
single-soliton limit. These characteristics are satisfied by the exact
two-soliton solution of the KdV-Sawada-Kotera equation: The deviation of this
solution from its KdV-type two-soliton approximation describes a purely
inelastic scattering process: The incoming state is the faster KdV soliton. It
propagates until it hits a localized perturbation, which causes its
transformation into the outgoing state, the slower soliton. In addition, the
effect of the perturbation on the exact two-soliton solution vanishes
identically in the single-soliton limit (equal wave numbers for the two
solitons).
