Laterally Coupled Diode Laser

[Tundragon]

Hi everyone, I am not sure if you guys can answer my question but I am currently looking into laterally coupled diode laser ,I am reading article about Coupling effects in the dynamic behavior of two laterally coupled semiconductor lasers
and I do fully understand some of the rate equation (1-5) but I do know the general meaning and the terms, just not how the author arrived at that particular outcome ,if you can help me I would be immensely grateful.

A link to article
https://www.researchgate.net/profile/Guillermo-Carpintero/publication/242101373_Coupling_effects_in_the_dynamic_behavior_of_two_laterally_coupled_semiconductor_lasers_3625-78/links/543d15b80cf2c432f7424901/Coupling-effects-in-the-dynamic-behavior-of-two-laterally-coupled-semiconductor-lasers-3625-78.pdf