We present an exact analytical solution by the use of an ansatz method for the modified nonlinear Schrödinger equation ${\mathrm{iU}}_{\zeta }+\frac{1}{2}\sigma U_{\tau \tau }{+N}^2|U{|}^2{U+isN}^2(|U{|}^2{U)}_{\tau }=0,$ describing the propagation of light pulses in optical fibers. The inclusion of the term ${\mathrm{isN}}^2(|U{|}^2{U)}_{\tau }$ in the usual nonlinear Schrödinger 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.

• Received 17 March 1997

DOI:https://doi.org/10.1103/PhysRevE.57.4751