GALILEAN SYMMETRY INVARIANT SOLUTIONS TO THE KDV-BURGERS EQUATION AND NONLINEAR SUPERPOSITION OF SHOCK WAVES - Y. I. Dementyev; A. V. Samokhin (Научный вестник МГТУ ГА)
A description of the Galilean symmetry invariant solutions to the KdV-Burgers equation is reduced to studying of phase trajectories of the corresponding ODE depending on a parameter (the velocity of a shock wave propagation). Exact invariant solutions are simple shock waves that become separatrixes on the phase portrait which always has two singular points for a given value of the parameter. For nonlinear superposition of shock waves the phase portrait contains four singular points; its consequent bifurcations lead to oscillations.