Analytical exploration and parametric insights into optical solitons in magneto-optic waveguides: Advances in nonlinear dynamics for applied sciences

Abstract Within this study, we delve into novel optical solitons concerning the perturbed nonlinear Schrödinger equation, which governs the propagation of electromagnetic waves in magneto-optic waveguides. These components play vital roles in optical transmission lines and lasers, serving critical functions within integrated optical circuits as circulators, modulators, and isolators. Employing the simplest equation method, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfenced open="(" close=")"> <m:mrow> <m:mfrac> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi>φ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>δ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:mfrac> <m:mo>,</m:mo> <m:mfrac> <m:mrow> <m:mi>φ</m:mi> <m:mo accent="false">′</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>δ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mi>φ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>δ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:mfrac> </m:mrow> </m:mfenced> </m:math> \left(\phantom{\rule[-0.75em]{}{0ex}},\frac{1}{\varphi \left(\delta )},\frac{\varphi ^{\prime} \left(\delta )}{\varphi \left(\delta )}\right) method, and the generalized Riccati equation mapping method, we derive single and multi-optical soliton solutions. Our analysis yields a diverse array of solutions, including multi-soliton, singular, combo bright-dark, periodic singular, bright, and dark optical solitons. Additionally, we discuss the parametric conditions crucial for both the existence and shaping of these solitons. The visual representation of our findings through three-dimensional, two-dimensional, and contour plots elucidates the dynamic phenomena and interprets the physical implications of these solutions using various parameter values. This research demonstrates the efficacy of rational analytical methods in elucidating the intricate dynamics of soliton solutions in nonlinear optical systems, thereby offering valuable insights for further exploration in the fields of physics, mathematics, sciences, and engineering.