Initial value problems of cylindrical electromagnetic waves propagation in a nonlinear nondispersive medium

We introduce a simple method to estimate the accuracy of exact solutions under initial value conditions proposed by Petrov and Kudrin [Phys. Rev. Lett. 104, 190404 (2010)]. We demonstrate that even for a sufficiently weak nonlinearity, the initial value condition difference between linear and nonlinear case may be evident. Our result may be used as a criterion of employing the exact solution to deal with initial value problems of cylindrical electromagnetic wave propagation in a nonlinear nondispersive medium.