Projection to orthogonal function basis method for nonlinear multi-mode fiber

Projecting to orthogonal function basis allow us to derive (without averaging across the fiber as e.g. in Kodama, Y., & Hasegawa, A., 1981, Proc. IEEE Vol. 69, pp. 1445.) coupled nonlinear Schrodinger equation (NLSE) for multi-mode fibers. The basis, which we introduce, by electromagnetic field expansion, for waveguide modes, depends on a waveguide geometry (we consider fiber with cylindrical geometry which correspond to Bessel function basis), in this paper we analyze fiber with a weak nonlinearity descent from the Kerr effect. We present analytical and numerical results for nonlinear coefficients of CNLS equations. Also we show numerical result for CNLS equations solution for two mode problem and we compare this results with experiment