Nonlinear dynamics of a model of interacting waves in a space with partially reflecting boundaries

We investigate numerically the spatio-temporal behavior of a bounded distributed nonlinear dynamical system of finite length that describes the interaction of two one-dimensional waves. The nonlinear and dispersion properties of the waves and conditions at the boundaries of the interaction space correspond to a simple case, when the electromagnetic wave in a waveguide interacts with the wave in the how of oscillating electrons. Typical spatial structures of the waves, their temporal behavior and bifurcational transitions in the parametric plane are examined on the basis of the qualitative analysis and statistical processing of the data of the computer experiments.