The Bilinear Formula in Soliton Theory of Optical Fibers

Abstract

Solitons are wave phenomena or pulses that can maintain their shape stability when propagating in a medium. In optical fibers, they become general solutions of the Non-Linear Schrödinger Equation (NLSE). Despite its mathematical complexity, NLSE has been an interesting issue. Soliton analysis and mathematical techniques to solve problems of the equation keep doing. Yan Chen (2022) introduced them based on bilinear formula for the case of the generalized NLSE extended models into third and fourth-order dispersions and cubic-quintic nonlinearity. In this paper, we review the form of the bilinear formula for the case. We re-observed a one-soliton solution based on the formula and verified the work of the last researcher. Here, the mathematical parameters of position α(0) and phase η are verified to become features of change in horizontal position and phase of one soliton in the (z, t) plane during propagation. In addition, we notice the soliton has established stability. Finally, for the condition Kerr effect focusing or the group velocity dispersion β2 more dominates, we present like the soliton trains in optical fibers under modulation instability of plane wave.

An Exact Solution of Nonlinear Schrödinger Equation in a Lossy Fiber System Using Direct Solution Method

“…Here, we consider soliton as the object of our studies. When the second term in ( 1) is positive, we work in an anomalous dispersion system where the soliton solution is a bright soliton (Agrawal, 2013;Saputra et al, 2022). Now, lets us solve Equation (1) using direct solution methods.…”

“…On the other hand, Liu et al (2022) have also studied the NLSE of fiber optic numerically using the split-time-step Crank-Nicolson method. Then, Saputra et al (2022) verified the bilinear formula for the NLSE problem.…”