Modulation Theory for Radially Symmetric Kink Waves Governed by a Multi-Dimensional Sine-Gordon Equation

Abstract We derive a modulation theory for the resolution of radially symmetric kink waves governed by multi-dimensional sine-Gordon equation. Whitham is developed to explain return an expanding wave, as well predicting its maximum expansion radius and time. Comparisons with full numerical solutions equation show that gives excellent predictions not only returning time radius, but also details itself. In addition, method can be extended dissipative equations generalized deal wide class initial conditions beyond kinks.