The scheme of fast ignition by super-intense laser of DT target placed at a cavity of the radiate plasma liner, created in a "dynamic - hohlraum" system is considered. It is shown that this scheme can supply effective TN fusion. The process of compression and preheating of DT fuel of shell target by X-ray radiation of Dynamic Hohlraum is simulated by the code TRITON with parameters of Z-generator of Sandia National Laboratory. The optimum parameters of target are obtained. The mechanism of ignitor creation by protons, accelerated by ultra-shot laser radiation is considered and corresponding laser parameters are evaluated. The mathematical simulation of the following thermonuclear (TN) burn wave propagation in DT target is carried out with the use of TERA code based upon the direct statistical simulation of kinetics of fast charged particles and quantum of thermal radiation on each time step of hydrodynamics. The released TN energy is obtained as a function of ignition energy. The theoretical explanations of obtained dependencies are presented. The laser parameters necessary to produce G≫1 are determined.