Chaotic dynamics of linear hyperbolic PDEs with nonlinear boundary conditions

The study of chaotic PDEs with variable coefficients involves higher level of complexity than for the ones with constant coefficients. In this paper, we investigate the chaotic oscillations of a one-dimensional second order linear hyperbolic PDE with variable coefficients that is factorizable as a product of two noncommutative first order operators and the boundary conditions at both ends of the PDE are general nonlinear. Numerical simulations are provided to illustrate the effectiveness of our theoretical results.