The hyperbolic nature of the zero dispersion Kdv limit

Strict hyperboiicity and genuine nonlinearity is proved for the zero dispersion KdV limit wherever the Riemann invariants, λk, remain distinct. more specifically, the characteristic speeds, sk , have the opposite ordering of the Riemann invariants and the derivative of a characteristic speed with respect to its corresponding Riemann invariant is negative A Riccati eqation is found for the evolution of ∂kλk along the kTM characteristic and some implications to breaking are discussed.