  We prove that line solitons of the two-dimensional hyperbolic nonlinear
Schr\"odinger equation are unstable with respect to transverse perturbations of
arbitrarily small periods, {\em i.e.}, short waves. The analysis is based on
the construction of Jost functions for the continuous spectrum of
Schr\"{o}dinger operators, the Sommerfeld radiation conditions, and the
Lyapunov--Schmidt decomposition. Precise asymptotic expressions for the
instability growth rate are derived in the limit of short periods.
