The wet dreams you experience, while asleep, do not break the fast as one has no control over it. Therefore, you only need to do ghusl in order to be able to perform salah, read the Qur'an, etc.

Having said this, I should also point out that the fast is broken by deliberate actions, inducing seminal emission- including lustful looks, watching the lewd acts or meditating upon them. While fasting, we must practice restraint. In other words, we ought to control our eyes, ears, speech and mind, as well as all other faculties.

I pray to Allah to help us protect our fasts by practicing restraint and mindfulness of Him.