Higher conditional symmetry and reduction of initial value problems (Q1610742)

In the reviewed article the author gives a self-contained exposition of the symmetry approach to reduce initial value problems for PDEs developed in previous author's works. He applies this approach for classification of initial value problems \[ u_t=u_{xxx}+F(t,x,u,u_x,u_{xx}),\quad (\alpha(x)u_x+\beta(x)u)|_{t=t_0}= \gamma(x) \] (\(F,\alpha,\beta,\gamma\) are smooth functions), which admit reduction to Cauchy problems for a system of two ordinary differental equations.