  The integro-differential wave equation for the probability density function
for a classical one-dimensional L\'evy walk with continuous sample paths has
been derived. This equation involves a classical wave operator together with
memory integrals describing the spatio-temporal coupling of the L\'evy walk. It
is valid for any running time PDF and it does not involve any long-time
large-scale approximations. It generalizes the well-known telegraph equation
obtained from the persistent random walk. Several non-Markovian cases are
considered when the particle's velocity alternates at the gamma and power-law
distributed random times.
