  In this work we present a new class of Runge-Kutta (RK) methods for solving
systems of hyperbolic equations with a particular structure, generalization of
a wave-equation. The new methods are {\it partially implicit} in the sense that
a proper subset of the equations of the system contains some terms which are
treated implicitly. These methods can be viewed as a particular case of the
implicit-explicit (IMEX) RK methods for systems of equations with wave-like
structure. For these systems, the optimal methods with the new structure are
easier to derive than the IMEX ones, specially when aiming at higher-order (up
to fourth-order in this work). The methods are constructed considering the
classical strong-stability-preserving optimal explicit RK methods for the
purely explicit part. The resulting partially implicit RK methods do not
require any inversion of operators and hence their computational cost per
iteration is similar to those of explicit RK methods. We analyse the stability
and convergence properties and show their practical applicability in several
numerical examples. Our results show that, compared with explicit RK methods,
the new methods have better stability properties (larger steps are allowed) and
in general show smaller discretization error.
