Monomorphisms of Free Burnside Groups

In the paper, it is proved that, for any odd $n\ge1039$, there are words $u(x,y)$ and $v(x,y)$ over the group alphabet $\{x,y\}$ such that, if $a$ and $b$ are any two noncommuting elements of the free Burnside group $B(m,n)$, then, for some $k$, the elements $u(a^k,b)$ and $v(a^k,b)$ freely generate a free Burnside subgroup of the group $B(m,n)$. In particular, the facts proved in the paper imply the uniform nonamenability of the group $B(m,n)$ for odd $n$, $n\ge1039$.