Stability of stationary solutions of the generalized KdV-Burgers equation

The stability of discontinuities representing solutions of a model generalized KdVЦBurgers equation with a nonmonotone potential is analyzed.The spectral (linear) stability of the structure of special discontinuities was previously studied. Here the spectral stability of nonspecial discontinuities is investigated. The structure of a nonspecial discontinuity represents a phase curve joining two special points: a saddle (the state ahead of the discontinuity) and a focus or node (the state behind the discontinuity). The set of nonspecial discontinuities is examined depending on the dispersion and dissipation parameters. A set of stable nonspecial discontinuities is found.