The N-soliton solution of a two-component modified nonlinear Schr\"odinger equation

The $N$-soliton solution is presented for a two-component modified nonlinear Schr"odinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.