Resonance in a driven two-level system: analytical results without the rotating wave approximation

We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cos\omega t,a(t)sin\omega t,\omega_0}, with a(t) \sim cn(\nu t,k). The problem is exactly analytically solvable and we propose the scheme for constructing the solutions. For all field configurations the resonance conditions are discussed. The explicit solutions for N=1,2 we obtained coincide at \omega=0 in the proper parameter domain with predictions of the rotating wave approximation and agree nicely with numerical calculations beyond it.