From polynomial integrals of Hamiltonian flows to a model of non-linear   elasticity
  We prove non existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Nonlinear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems. 
Michael Bialy and Andrey E. Mironov
math.AP nlin.SI