Application-oriented analysis of nonlinear water waves via analytical and neural network approaches; Oceanography Advances
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Application-oriented analysis of nonlinear water waves via analytical and neural network approaches; Oceanography Advances
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
AIMS Mathematics
ISSN
2473-6988
e-ISSN
2473-6988
Volume of the periodical
10
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
31
Pages from-to
27635-27665
UT code for WoS article
001628334500009
EID of the result in the Scopus database
2-s2.0-105022939108