ANALYTICAL SOLUTION FOR THE MODIFIED NONLINEAR SCHRODINGER-EQUATION DESCRIBING OPTICAL SHOCK FORMATION

We present an exact analytical solution by the use of an ansatz method for the modified nonlinear Schrodinger equation iU(zeta)+1/2 sigma U- tau tau+N-2\U\U-2+isN(2)(\U\U-2)(tau) = 0, describing the propagation of light pulses in optical fibers. The inclusion of the term is N-2(\U \U-2)(tau) in the usual nonlinear Schrodinger equation arises from an intensity-dependent group velocity and produces a temporal pulse disto rtion leading to the development of an optical shock. Previous work [X u Bingzhen and Wang Wenzheng, Phys. Rev. E 51, 1493 (1995)] using the traveling-wave method does not exhibit this important physical picture .