On the Movement of Excitation Wave Breaks

Movement of excitation waves in active media, in some cases, can be described by a kinematic approach in terms of the movement of curves, the wave crests, by neglecting other details such as wave profiles and refractoriness. Of special interest are broken waves, e.g., spiral waves. In this case, additional equations for the wave tip movement are required. We derive such equations by singular perturbation techniques. These equations differ from those proposed earlier from semi-phenomenological arguments [10] and [11] , are more complicated and diverse and admit a broader variety of solutions. As an illustration, we apply these equations to the problem of a stationary rotating spiral wave. In this particular example, the traditional equations have happened to be a special case.