ИСТИНА

We investigate the mode of laser pulse propagation in homogeneous medium with multi-photon absorption at which the shape of pulse(or beam) is self-similar one along some distance of propagation. Finding the shape of laser pulse with such property is based on the solution of nonlinear eigenfunction problem for Schrödinger equation with nonlinear absorption. Under certain conditions this eigenfunction gives us the pulse shape with requiring properties. We develop also analytical solution of corresponding problem with confirms our computer simulation results. We consider both pure absorption medium and medium with multi-photon absorption and nonlinear refraction.