New wave behaviors of the Fokas-Lenells model using three integration techniques

Abstract

In this investigation, we apply the improved Kudryashov, the novel Kudryashov, and the unified methods to demonstrate new wave behaviors of the Fokas-Lenells nonlinear waveform arising in birefringent fibers. Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. These solutions encompass periodic waves with W-shaped profiles, gradually increasing amplitudes, rapidly increasing amplitudes, double-periodic waves, and breather waves with symmetrical or asymmetrical amplitudes. Singular solitons with single and multiple breather waves are also derived. Based on these findings, we can say that our implemented methods are more reliable and useful when retrieving optical soliton results for complicated nonlinear systems. Various potential features of the derived solutions are presented graphically.

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

“…Its significance in research drives the exploration of diverse forms of OSs. Multiple methodologies have been established to generate OS solutions for such models, including the modified (G′/G)-expansion method 8 – 10 , the unified method 11 , 12 , the modified double Laplace transform scheme 13 , the adapted exponential task scheme 14 , the symbolic computational approach 15 , generalized Riccati equation mapping 16 , mapping method 17 , the φ6-model expansion approach 18 , sine–Gordon expansion method 19 , the improved Kudryashov’s approach 20 , Lie symmetry analysis 21 , the New generalized auxiliary equation method 22 , binary Darboux transformations 23 , among many others.…”