Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10257937" target="_blank" >RIV/61989100:27740/25:10257937 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818125001597" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818125001597</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2025.101232" target="_blank" >10.1016/j.padiff.2025.101232</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation

Popis výsledku v původním jazyce

In this study, the fractional-stochastic Fokas-Lenells equation is considered in the Stratonovich framework. The new extended direct algebraic method is applied to construct various types of fractional solutions, including trigonometric, complex, hyperbolic, and exponential forms. Given the equation&apos;s broad applications in telecommunication systems, complex system theory, quantum field theory, and quantum mechanics, the derived solutions have potential to model a variety of significant physical phenomena. To further illustrate the influence of multiplicative noise and fractional derivatives, multiple 3D plots are presented, highlighting their impact on the analytical behavior of the system. Secondly, by applying a Galilean transformation, the model is reformulated into a planar dynamical system, allowing for in-depth qualitative analysis. The sensitivity analysis of the model is performed, along with an examination of quasi-periodic patterns emerging from perturbations. The simulation results reveal that adjusting the amplitude and frequency parameters significantly alters the dynamic behavior of the system. The quasi-periodic behavior is further analyzed through time analysis, multi-stability, and Lyapunov exponents. Our results highlight the impact of the method on system dynamics and demonstrate its effectiveness in studying solitons and phase behavior in nonlinear models. These findings offer new insights into how the proposed approach can induce significant changes in system dynamics, emphasizing its utility in the analysis of soliton solutions and phase visualizations in various nonlinear models. By generating state-dependent oscillations, multiplicative noise has a substantial impact on the dynamics of the system. These fluctuations can either improve or decrease stability and result in complicated behaviors. The completion of stochastic systems affected by internal or external noise sources requires an understanding of this interaction. © 2025 The Author(s)

Název v anglickém jazyce

Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation

Popis výsledku anglicky

In this study, the fractional-stochastic Fokas-Lenells equation is considered in the Stratonovich framework. The new extended direct algebraic method is applied to construct various types of fractional solutions, including trigonometric, complex, hyperbolic, and exponential forms. Given the equation&apos;s broad applications in telecommunication systems, complex system theory, quantum field theory, and quantum mechanics, the derived solutions have potential to model a variety of significant physical phenomena. To further illustrate the influence of multiplicative noise and fractional derivatives, multiple 3D plots are presented, highlighting their impact on the analytical behavior of the system. Secondly, by applying a Galilean transformation, the model is reformulated into a planar dynamical system, allowing for in-depth qualitative analysis. The sensitivity analysis of the model is performed, along with an examination of quasi-periodic patterns emerging from perturbations. The simulation results reveal that adjusting the amplitude and frequency parameters significantly alters the dynamic behavior of the system. The quasi-periodic behavior is further analyzed through time analysis, multi-stability, and Lyapunov exponents. Our results highlight the impact of the method on system dynamics and demonstrate its effectiveness in studying solitons and phase behavior in nonlinear models. These findings offer new insights into how the proposed approach can induce significant changes in system dynamics, emphasizing its utility in the analysis of soliton solutions and phase visualizations in various nonlinear models. By generating state-dependent oscillations, multiplicative noise has a substantial impact on the dynamics of the system. These fluctuations can either improve or decrease stability and result in complicated behaviors. The completion of stochastic systems affected by internal or external noise sources requires an understanding of this interaction. © 2025 The Author(s)

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Partial Differential Equations in Applied Mathematics

ISSN

2666-8181

e-ISSN

2666-8181

Svazek periodika

14

Číslo periodika v rámci svazku

June

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

101232

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-105007529978