Quasilinear systems with linearizable characteristic webs
  We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic webs on all solutions imposes simple second-order constraints for the characteristic speeds of the system. It is demonstrated that every such system with n>3 components can be transformed by a reciprocal transformation to n uncoupled Hopf equations. All our considerations are local. 
S.I.Agafonov, E.V.Ferapontov and V.S.Novikov
math.DG