Traveling wave solutions for the hyperbolic Cahn-Allen equation

Traveling wave solutions of the hyperbolic Cahn-Allen equation are obtained using the first integral method, which follows from well-known Hilbert-Nullstellensatz theorem. The obtained complete class of traveling waves consists of continual and singular solutions. Continual solutions are represented by tanh -profiles and singular solutions exhibit unbounded discontinuity at the origin of coordinate system. With the neglecting inertia of the dynamical system, the obtained traveling waves include the previous solutions for the parabolic Cahn-Allen equation.