A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.
© 1993 Optical Society of America
Shiva Kumar, G. V. Anand, and A. Selvarajan, "Spectral approach for the soliton and periodic solutions of the nonlinear wave equation," J. Opt. Soc. Am. B 10, 697-703 (1993)