A note concerning hyperbolic equations with constant coefficients

James F. Heyda
1960 Quarterly of Applied Mathematics  
The canonical form of the linear, homogeneous hyperbolic partial differential equation in two independent variables is uxy + aux + buv + cu = 0, where a, b, c are functions of x, y. The constant coefficients case, frequently met in applitions, can be reduced to the simpler form vxu -\v = 0, X = ab -c with X constant, through the substitution v(x, y) -u exp (bx + ay). The solution of the Cauchy problem for an equivalent form of (2) with v and dv/dn prescribed along C is worked out explicitly by Copson [1] using the methods of M. Riesz. Fig. 1
doi:10.1090/qam/114044 fatcat:rq3jzetlineqhp4kzqd2yxtc4a