The compositional inverses of permutation polynomials of the form ${\sum }_{i=1}^k{b}_i(x^{p^m}+x+\delta {)}^{s_i}-x$ over ${\mathbb{F}}_{p^{2m}}$

In this paper, we present the compositional inverses of several classes permutation polynomials of the form ${\sum }_{i=1}^k{b}_i(x^{p^m}+x+\delta {)}^{s_i}-x$ over ${\mathbb{F}}_{p^{2m}}$, where for $1\le i\le k,$ $s_i,m$ are positive integers, $b_i,\delta \in {\mathbb{F}}_{p^{2m}},$ and $p$ is prime.