Analytical description of the structure of special discontinuities described by a generalized KdV-Burgers equation

Traveling wave solutions of a generalized KdV-Burgers equation are studied. The nonlinearity is specified as a piecewise linear flux function consisting of four parts. A boundary value shock-structure problem is solved. An analytical solution describing the structures of special discontinuities (undercompressive shocks) is obtained, and the behavior of these solutions is examined for various parameters of the problem.