Exploring analytical solutions and modulation instability for the nonlinear fractional Gilson–Pickering equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10254113" target="_blank" >RIV/61989100:27740/24:10254113 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2211379724000676?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2211379724000676?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.rinp.2024.107385" target="_blank" >10.1016/j.rinp.2024.107385</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exploring analytical solutions and modulation instability for the nonlinear fractional Gilson–Pickering equation

Popis výsledku v původním jazyce

The primary goal of this research is to explore the complex dynamics of wave propagation as described by the nonlinear fractional Gilson-Pickering equation (fGPE), a pivotal model in plasma physics and crystal lattice theory. Two alternative fractional derivatives, termed β and M-truncated, are employed in the analysis. The new auxiliary equation method (NAEM) is applied to create diverse explicit solutions for surface waves in the given equation. This study includes a comparative evaluation of these solutions using different types of fractional derivatives. The derived solutions of the nonlinear fGPE, which include unique forms like dark, bright, and periodic solitary waves, are visually represented through 3D and 2D graphs. These visualizations highlight the shapes and behaviors of the solutions, indicating significant implications for industry and innovation. The proposed method&apos;s ability to provide analytical solutions demonstrates its effectiveness and reliability in analyzing nonlinear models across various scientific and technical domains. A comprehensive sensitivity analysis is conducted on the dynamical system of the fGPE. Additionally, modulation instability analysis is used to assess the model&apos;s stability, confirming its robustness. This analysis verifies the stability and accuracy of all derived solutions.

Název v anglickém jazyce

Exploring analytical solutions and modulation instability for the nonlinear fractional Gilson–Pickering equation

Popis výsledku anglicky

The primary goal of this research is to explore the complex dynamics of wave propagation as described by the nonlinear fractional Gilson-Pickering equation (fGPE), a pivotal model in plasma physics and crystal lattice theory. Two alternative fractional derivatives, termed β and M-truncated, are employed in the analysis. The new auxiliary equation method (NAEM) is applied to create diverse explicit solutions for surface waves in the given equation. This study includes a comparative evaluation of these solutions using different types of fractional derivatives. The derived solutions of the nonlinear fGPE, which include unique forms like dark, bright, and periodic solitary waves, are visually represented through 3D and 2D graphs. These visualizations highlight the shapes and behaviors of the solutions, indicating significant implications for industry and innovation. The proposed method&apos;s ability to provide analytical solutions demonstrates its effectiveness and reliability in analyzing nonlinear models across various scientific and technical domains. A comprehensive sensitivity analysis is conducted on the dynamical system of the fGPE. Additionally, modulation instability analysis is used to assess the model&apos;s stability, confirming its robustness. This analysis verifies the stability and accuracy of all derived solutions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

—

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Results in Physics

ISSN

2211-3797

e-ISSN

2211-3797

Svazek periodika

57

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

001179230400001

EID výsledku v databázi Scopus

2-s2.0-85183988370