Symmetry nonintegrability for extended $K(m,n,p)$ equation

Abstract

In the present paper we study symmetries of extended $K(m,n,p)$ equation $$ u_t=a(u^p)_{xxxxx}+b(u^n)_{xxx} + c(u^m)_{x} + f(u), $$ where $a,b,c$ are arbitrary real constants and $m,n,p$ are arbitrary integers, and prove that for $a\neq 0$ and $p\neq 1,-4$ this equation has no generalized symmetries of order greater than five and hence is not symmetry integrable.