Birkhoff Normal Form and Long Time Existence for d-Dimensional Generalized Pochhammer–Chree Equation

This paper is devoted to the proof of the long time existence results for the generalized Pochhammer–Chree equation on the irrational torus \(\mathbb {T}^d_{\eta }\) and the rational torus \(\mathbb {T}^d_{\zeta }\) by using Birkhoff normal form technique, the so-called \({ tame}\) property of the nonlinearity and a careful analysis of the frequency.