Geometry of pseudopotentials of a third order evolution equation. (Q1599422)

The author considers the geometry of a third order evolution equation \[ u_t=f(t, x^1,\dots,x^n,u,u_j,u_{jk},u_{jkl})\;(j,k,l=1, \dots,n), \] where \(u\) is an unknown function, \(u_t\) is its derivate in respect with time \(t\), \(u_i\) are partial derivatives with respect to spatial variables and the function \(f\) does not depend on \(u_t\). The problem of existence of pseudopotentials is also studied. The author uses the method suggested in \textit{A. K. Rybnikov} [ibid. 1995, No.\,5, 55--67 (1995; Zbl 0847.58073)] for studying the second-order evolution equations as the obtained results generalize the results obtain in that paper in the case of higher order equations.