Train to Copenhagen

I wouldn't count on it. Trains seem to be running on a completely different route all week. It would be odd if they planned track work on the main line for a week, let contracts and rerouted all the trains and then said "Oh, never mind."

When checking on www.sj.se I see that there are a few non stop trains. Tickets appear not to be yet available for that train. It is after all very early.

Trains do not sell out months in advance. If you are looking now at a train in June and see a mention that tickets are sold out what is really going on is that the seat inventory has not been loaded yet.

Even the one direct train showing for June 13 takes 2 hours longer than normal because of the diversion to an alternate route. I think WengenK means direct, as there are no nonstops.

Maybe. It seems like sj.se reroutes you via Västergötland due to maintenance on the route east of Vättern. But I haven't found out what exactly is planned. So it might mean that the line is completely closed, in that case the route via Gothenburg will be the only option. Which in itself is not a bad thing, Gothenburg is well worth a stop. But there also seem to be a direct train in around 7 hours via Falköping-Borås, which suggests that the main line east of Vättern is completely closed that day.

There is a 12:26 direct departure just over 7 hours. The timetable also shows a 6:30 departure that SJ isn't showing, so it is unknown if they add it later. I will fly that week in the other direction, a noon flight is better for my sleep than a 6:30 train departure. You could consider the night train, it terminates in Malmö where you can take a frequent commuter train to Copenhagen.