This paper investigates the generation of plasma wave and third harmonic generation in hot collision less plasma by a Gaussian ultra intense laser beam, when relativistic and ponderomotive nonlinearities are operative. First, we derive the dynamical equation for the pump laser beam when these two nonlinearities are operative. The solution of pump laser beam has been obtained within the paraxial ray approximation. Filamentary structures of the laser beam are observed. On account of V→ × B→ force, the generation of plasma wave at second harmonic frequency has been studied in these filamentary structures. Interaction of the plasma wave with the incident laser beam generates the third harmonic. For the typical laser plasma parameters: Nd: YAG laser beam (λ = 1064 nm), ro = 15 µm, laser power flux equals 6 × 1017 W/cm2, electron density equals no = 1.9 × 1019 per cm3, the third harmonic yield comes out to be equals to 2 × 10−6.
