<p>In this manuscript, several complex optical phenomena depending extensively on the space-time fractional Biswas–Arshed equation with the beta derivative are specified. The incorporation of fractional derivatives enables a more accurate representation of physical systems that exhibit memory effects and non-linear interactions. To examine this fractional nonlinear model, we employ the modified Sardar sub-equation method, which has proven effective for handling nonlinear evolution equations of fractional order. The Biswas–Arshed model plays a vital role in the study of photonic crystals and advanced optical materials, offering new avenues for controlling light propagation and designing photonic devices. A diverse set of soliton solutions is obtained, including dark compacton solitons, singular kink solitons, bright compacton solitons, anti-kink solitons, stumpons solitons, anti-bell-shaped (topological) solitons, compositive wave solutions, anti-peaked solitons with decay, bell-shaped (non-topological) solitons, cusped periodic solitons, kink solitons, line rough waves, multiple kink structures, periodic solitons with anti-peaked crests and troughs, smooth periodic solitons, and mixed kink-periodic soliton solutions. The influence of the fractional-order parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40509_2025_366_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> on waveform structures is analyzed using three-dimensional, two-dimensional, and contour plots generated in <Emphasis FontCategory="NonProportional">Maple</Emphasis> and <Emphasis FontCategory="NonProportional">Mathematica</Emphasis>. The study highlights how variations in both primary and auxiliary parameters significantly affect the morphology and dynamics of the solitons. The results demonstrate the robustness, versatility, and computational efficiency of the modified Sardar sub-equation method for solving space-time fractional evolution equations. Researchers and engineers in the domains of nonlinear optics, optical solitons, ultrafast optical signals, nonlinear photonics, quantum optics, biophotonics, and photonic crystals will find this study to be beneficial. It helps individuals comprehend the applications in these fields better, which empowers them to make wiser and more efficient choices.</p>

Soliton dynamics in the fractional nonlinear model with applications in new photonic devices

期刊论文
发表日期：

2025年5月31日

查看全文

Umair Asghar,
Muhammad Imran Asjad,
Suhad Ali Osman Abdallah

摘要

In this manuscript, several complex optical phenomena depending extensively on the space-time fractional Biswas–Arshed equation with the beta derivative are specified. The incorporation of fractional derivatives enables a more accurate representation of physical systems that exhibit memory effects and non-linear interactions. To examine this fractional nonlinear model, we employ the modified Sardar sub-equation method, which has proven effective for handling nonlinear evolution equations of fractional order. The Biswas–Arshed model plays a vital role in the study of photonic crystals and advanced optical materials, offering new avenues for controlling light propagation and designing photonic devices. A diverse set of soliton solutions is obtained, including dark compacton solitons, singular kink solitons, bright compacton solitons, anti-kink solitons, stumpons solitons, anti-bell-shaped (topological) solitons, compositive wave solutions, anti-peaked solitons with decay, bell-shaped (non-topological) solitons, cusped periodic solitons, kink solitons, line rough waves, multiple kink structures, periodic solitons with anti-peaked crests and troughs, smooth periodic solitons, and mixed kink-periodic soliton solutions. The influence of the fractional-order parameter $\omega $ $ω$ on waveform structures is analyzed using three-dimensional, two-dimensional, and contour plots generated in Maple and Mathematica. The study highlights how variations in both primary and auxiliary parameters significantly affect the morphology and dynamics of the solitons. The results demonstrate the robustness, versatility, and computational efficiency of the modified Sardar sub-equation method for solving space-time fractional evolution equations. Researchers and engineers in the domains of nonlinear optics, optical solitons, ultrafast optical signals, nonlinear photonics, quantum optics, biophotonics, and photonic crystals will find this study to be beneficial. It helps individuals comprehend the applications in these fields better, which empowers them to make wiser and more efficient choices.