Halyna LAHNO 1 and Volodymyr SMALIJ2
1Poltava State Pedagogical University,
 2 Ostrogradskoho Str.,
2National Agricultural University,
E-mail: laggo@poltava.bank.gov.ua

On equations of Korteweg-de Vries type with highest symmetry properties

The problem of existence of nonlinear equations among the set of equations $u_t=u_{xxx}+F(t,x,u, u_x, u_{xx})$ are considered which have highest symmetry and are known in different applications of Korteweg-de Vries equation.