Let’s consider L(u) = a(x, t)utt + b(x, t)utx + c(x, t)uxx + d(x, t)ut + h(x, t)ux, x ∈ R1. The second order quasilinear equations are studied in the following form: L(u) + r(u) a(x, t)u 2 t + b(x, t)utux + c(x, t)u 2 x + ...