Whether you need a special visa or residence permit to study abroad depends on your own citizenship as well as your destination. Different rules may apply to Danish and international students at SDU. It is important that you check the visa requirements by contacting the host university or the embassy of the country in question. Normally it is a mere formality to get a visa once you can document that you have been enrolled at a university within the country.
If you are an EU citizen and travel within the EU, you will normally only have to get a residence permit after arrival in the host country.
Outside the EU you will most likely have to apply for a visa, and normally you will be informed by the host university.
Non-Danish citizens: check your residence permit
If you are a non-Danish citizen, we strongly recommend that you check up on whether or not your residence permit (regardless of type) allows you to leave and return to Denmark, or whether you need to apply for a new one.
This is important regardless of your citizenship (EU/non-EU) and duration of exchange stay.
If you are in doubt, please contact the authorities directly - you can find the contact information on newtodenmark.dk.