Abstract: Some natures have been studied for the propagation process of very intense and very short laser pulse in underdense plasma.The wave equation is derived and solved using the method of 2-D Fast Fourier Transformation.The basic equations for relativistic self-focusing include the nonlinear source term and the effect of diffraction.As a result of ponderomotive forces and relativism,the plasma frequency is reduced and so the refractive index is changed.It affects the propagation of laser in plasma.When the incident laser power (p) exceeds the critical power (p_c),self-focusing appears during the propagation of laser.On the contrary,laser damps gradually and self-focusing doesn't appear.

Key words: laser, plasmas, relativism, filamentation, numerical simulation