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…