Analytical solution for the modified nonlinear Schrodinger equation describing optical shock formation

摘要

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-2UU-2+isN(2)(UU-2)(tau) = 0, describing the propagation of light pulses in optical fibers. The inclusion of the term is N-2(UU-2)(tau) in the usual nonlinear Schrodinger equation arises from an intensity-dependent group velocity and produces a temporal pulse distortion leading to the development of an optical shock. Previous work [Xu Bingzhen and Wang Wenzheng, Phys. Rev. E 51, 1493 (1995)] using the traveling-wave method does not exhibit this important physical picture. [References: 21]