See formula (39) : https://www.scielo.br/j/rbef/a/wh9hgMSRTJzvws8ZxzL8NNp/?format=pdf&lang=en

with :$\beta= tanh(\varphi)\;\;,\gamma=cosh(\varphi)\;\;, \beta\gamma = sinh(\varphi)$

https://en.wikipedia.org/wiki/Lorentz_transformation

we have:

$x'^{+}=\gamma(x^{+}-\beta x^{+})$

$ x'^{-}=\gamma(x^{-}-\beta x^{-}) $

See formula (39) : https://www.scielo.br/j/rbef/a/wh9hgMSRTJzvws8ZxzL8NNp/?format=pdf&lang=en

with :$\beta= tanh(\varphi)\;\;,\gamma=cosh(\varphi)\;\;, \beta\gamma = sinh(\varphi)$

https://en.wikipedia.org/wiki/Lorentz_transformation

we have:

$x'^{+}=\gamma(x^{+}-\beta x^{+})$

$ x'^{-}=\gamma(x^{-}+\beta x^{-}) $