Application-oriented analysis of nonlinear water waves via analytical and neural network approaches; Oceanography Advances

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10259109" target="_blank" >RIV/61989100:27740/25:10259109 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.aimspress.com/article/id/6926d52fba35de55f26bed65" target="_blank" >https://www.aimspress.com/article/id/6926d52fba35de55f26bed65</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/math.20251215" target="_blank" >10.3934/math.20251215</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Application-oriented analysis of nonlinear water waves via analytical and neural network approaches; Oceanography Advances

Popis výsledku v původním jazyce

The fifth-order nonlinear water wave equation was explored in this and its utility in oceanography and its continued establishment was highlighted. Lie symmetry theory was applied to the nonlinear model, and the corresponding infinitesimal generators were constructed. Using the theory of abelian algebra and a suitable process of similarity reduction, the governing equation was simplified to a nonlinear ordinary differential equation. A new extended algebraic method, the nonlinear evolutionary differential approximation method, was presented to obtain the wave profiles by formulation of very general analytical solutions. To get a more detailed idea of how the physical processes that include nonlinear water waves work, 2D and 3D plots were created for several sets of parameter values, showing how the solitons were formed with unique shapes and the combined effects of dispersion and nonlinearly. In addition, a physics-informed neural network was deployed for the analysis of wave profiles. In this context, a 3D graphical representation was depicted with 2D training graphs. Additionally, by use of traveling wave transformation, 2D plots were presented to show how the wave profiles vary when parameter changes. The results, were obtained when the physics-informed neural network, were validated with a numerical scheme and revealed that the variation of parameters is crucially important to nonlinear oceanographic theories. These results support adequate parameter choices in the modeling of wave propagation and interaction in nonlinear water waves.

Název v anglickém jazyce

Application-oriented analysis of nonlinear water waves via analytical and neural network approaches; Oceanography Advances

Popis výsledku anglicky

The fifth-order nonlinear water wave equation was explored in this and its utility in oceanography and its continued establishment was highlighted. Lie symmetry theory was applied to the nonlinear model, and the corresponding infinitesimal generators were constructed. Using the theory of abelian algebra and a suitable process of similarity reduction, the governing equation was simplified to a nonlinear ordinary differential equation. A new extended algebraic method, the nonlinear evolutionary differential approximation method, was presented to obtain the wave profiles by formulation of very general analytical solutions. To get a more detailed idea of how the physical processes that include nonlinear water waves work, 2D and 3D plots were created for several sets of parameter values, showing how the solitons were formed with unique shapes and the combined effects of dispersion and nonlinearly. In addition, a physics-informed neural network was deployed for the analysis of wave profiles. In this context, a 3D graphical representation was depicted with 2D training graphs. Additionally, by use of traveling wave transformation, 2D plots were presented to show how the wave profiles vary when parameter changes. The results, were obtained when the physics-informed neural network, were validated with a numerical scheme and revealed that the variation of parameters is crucially important to nonlinear oceanographic theories. These results support adequate parameter choices in the modeling of wave propagation and interaction in nonlinear water waves.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

AIMS Mathematics

ISSN

2473-6988

e-ISSN

2473-6988

Svazek periodika

10

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

27635-27665

Kód UT WoS článku

001628334500009

EID výsledku v databázi Scopus

2-s2.0-105022939108