Numerical Study of Hyperbolic Equations with Integral Constraints Arising in Semiconductor Theory

An efficient numerical scheme is described for the solution of certain types of nonlinear hyperbolic equations with an integral constraint which are used to model the Gunn effect in semiconductors with impurity capture. We analyze the stability and convergence properties of the scheme and present the results of numerical simulations. Depending on the value of the parameters defining the problem, a great variety of solutions are obtained, including periodic recycling of solitary waves and chaotic regimes.