Integrable equations and classical S-matrix
  We study amplitudes of five-wave interactions for evolution Hamiltonian equations differ from the KdV equation by the form of dispersion law. We find that five-wave amplitude is canceled for all three known equations (KdV, Benjamin-Ono and equation of intermediate waves) and for two new equations which are natural generalizations of mentioned above. 
V.E Zakharov, A.V Odesskii, M. Onorato, M. Cisternino
nlin.SI math-ph math.MP