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 $a\ne 0$ and $p\ne 1,-4$ this equation has no generalized symmetries of order greater than five and hence is not symmetry integrable.

4 pages, no figures