Cylindrical coordinate of Galilean transformation

[Pring]

$r\rightarrow r-2qz$ and $\psi\rightarrow\psi+q\cdot(r-qz)$, I don't know how to derive it, anybody know?

This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

 

[jedishrfu]

Does the expression or theorem have a name? Perhaps you can search on it to see what pops up.