  The sine-Gordon equation in light cone coordinates is solved when Dirichlet
conditions on the L-shape boundaries of the strip [0,T]X[0,infinity) are
prescribed in a class of functions that vanish (mod 2 pi) for large x at
initial time. The method is based on the inverse spectral transform (IST) for
the Schroedinger spectral problem on the semi-line solved as a Hilbert boundary
value problem. Contrarily to what occurs when using the Zakharov-Shabat
eigenvalue problem, the spectral transform is regular and in particular the
discrete spectrum contains a finite number of eigenvalues (and no accumulation
point).
