Abstract
Singularities of solutions with steady structure of divergent quasi-linear third order equations proposed in /1/ are investigated. These equations written for functions of two independent variables, viz. space coordinate and time, simulate physical processes with dissipation and nonlinear and oscillatory effects. They define, in particular, unsteady potential motions in a layer of incompressible fluid with a free surface, for instance, unsteady plane jets or surface waves on shallow water. Another domain of their application is the investigation of properties of certain difference schemes of second order approximation in which similar equations are obtained as respective differential approximations of investigated schemes.
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