Dynamics of fractional optical solitary waves to the cubic-quintic coupled nonlinear Helmholtz equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255240" target="_blank" >RIV/61989100:27740/24:10255240 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818124001980?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818124001980?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2024.100812" target="_blank" >10.1016/j.padiff.2024.100812</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dynamics of fractional optical solitary waves to the cubic-quintic coupled nonlinear Helmholtz equation

Popis výsledku v původním jazyce

This work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects. The evolution of broad multicomponent self-trapping beams in Kerr-type nonlinear media is described by the coupled Helmholtz equation, which also take into account spatial dispersion due to non-paraxial effects. This phenomena is particularly relevant to the progressive miniaturization of optics, where the optical wavelength is similar to the beam width. It is essential to integrate non-Kerr terms, such as the self-steepening and the self frequency shift, into the coupled Helmholtz system in order to investigate the propagation of ultrashort optical pulses in the non-paraxial domain. For optical wave solutions, nonlinear ordinary equation of the governing model is achieved by applying the fractional transformation. The different types of the solutions like bright, dark, singular and mixed type solitons are extracted by applying advanced integration methods, namely modified Sardar subequation method and new Kudryashov method. These solutions provide very useful information on how the system operates. The applied approaches are highly efficient and have significant computational capability to efficiently tackle the nonlinear systems. Additionally, we include a diverse array of graphs to demonstrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. In the context of the proposed model, these visualizations assist with a comprehensive understanding of the solution&apos;s behavior and characteristics. It is anticipated that these solutions may be significant in the study of wave propagation and related fields. (C) 2024 The Authors

Název v anglickém jazyce

Dynamics of fractional optical solitary waves to the cubic-quintic coupled nonlinear Helmholtz equation

Popis výsledku anglicky

This work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects. The evolution of broad multicomponent self-trapping beams in Kerr-type nonlinear media is described by the coupled Helmholtz equation, which also take into account spatial dispersion due to non-paraxial effects. This phenomena is particularly relevant to the progressive miniaturization of optics, where the optical wavelength is similar to the beam width. It is essential to integrate non-Kerr terms, such as the self-steepening and the self frequency shift, into the coupled Helmholtz system in order to investigate the propagation of ultrashort optical pulses in the non-paraxial domain. For optical wave solutions, nonlinear ordinary equation of the governing model is achieved by applying the fractional transformation. The different types of the solutions like bright, dark, singular and mixed type solitons are extracted by applying advanced integration methods, namely modified Sardar subequation method and new Kudryashov method. These solutions provide very useful information on how the system operates. The applied approaches are highly efficient and have significant computational capability to efficiently tackle the nonlinear systems. Additionally, we include a diverse array of graphs to demonstrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. In the context of the proposed model, these visualizations assist with a comprehensive understanding of the solution&apos;s behavior and characteristics. It is anticipated that these solutions may be significant in the study of wave propagation and related fields. (C) 2024 The Authors

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2024

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

11

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85198732120