Quiescent Optical Solitons with Cubic–Quartic and Generalized Cubic–Quartic Nonlinearity

Abstract

The enhanced Kudryashov’s approach retrieves quiescent bright, dark, and singular solitons to the governing model that is considered with cubic–quartic form of self-phase modulation. The algorithm however fails to retrieve stationary solitons when the nonlinearity is the generalized version of the cubic–quartic form. The current analysis is conducted with a direct approach without an intermediary phase-portrait analysis as in the past.

Quiescent optical solitons for Fokas–Lenells equation with nonlinear chromatic dispersion and a couple of self-phase modulation structures

“…Step-3: Through the amalgamation of Equation (7) with Equations ( 8) and ( 9), followed by their substitution into Equation (3), we arrive at a polynomial equation encompassing the variables F(ξ ) and G(ξ ). The coefficients derived from this polynomial equation furnish the parameter values for Eqs.…”

“…The evolution of quiescent optical solitons has gained momentum and extreme importance ever since its first appearance about two decades ago [1][2][3][4][5]. The study of such solitons with nonlinear chromatic dispersion (CD) revealed quite a few results that have been reported all across the board [6][7][8][9][10]. Several models with nonlinear CD and various forms of self-phase modulation (SPM) structures have been studied [11][12][13][14][15].…”