Is it an obligation to have actual team (more than 1 person) to use RUP or can be RUP schema followed by only one man? Why ?
You want to use Rational Unified Process in a one-person team? While I suppose it might be a hint about the sorts of things that you're going to have to do, it would seem to me to be an absurdly heavyweight thing to use formally. Like using a thermonuclear weapon to kill a mosquito, it will work but is still Doing It Wrong.
For a single person team, test-driven development is almost certainly a better choice, as it helps you focus on being immediately productive (and hence on staying motivated, the big long-term problem). You don't need a great deal more than that because you don't have to worry about problems like lack of communication between development teams…
I think it might be reasonable if you cannot estabilish a team for trying out a process. But practically, you would certainly want to adjust it to remove artifacts, which are used for communication, which you will not need. You should also bear in mind, that it might be hard to act objectively especially in testing and all other review activities.