A quasilinear hyperbolic system of two first-order equations is introduced.
The system is linearized by means of the hodograph transformation combined
with Riemann's method of characteristics. In the process of linearization,
the main step is to explicitly express the characteristic velocities in te
rms of the Riemann invariants. The procedure is shown to be performed by qu
adrature only for specific combinations of the parameters in the system. We
then apply the method developed here to the dispersionless versions of the
typical coupled Korteweg-de Vries (cKdV) equations including the Broer-Kau
p, Ito, Hirota-Satsuma, and Bogoyavlenskii equations and show that these eq
uations are transformed into the classical Euler-Darboux equation. A more g
eneral quasilinear system of equations is also considered with application
to the dispersionless cKdV equations for the Jaulent-Miodek and Nutku-Oguz
equations. (C) 2001 American Institute of Physics.