  We generalize the projection to orthogonal function basis (including
polarization modes) method for nonlinear (Kerr medium) fiber and use this
method in a case of two-mode waveguide. We consider orthogonal Bessel functions
basis that fit the choice of cylindrical geometry of a fiber. The coupled
nonlinear Schr\"{o}dinger equations (CNLS) are derived. Analytic expressions
and numerical results for coupling coefficients are given; the fiber parameters
dependence is illustrated by plots.
