Comparative analysis of lump, breather, and interaction solutions using a bidirectional data mapping approach
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10259594" target="_blank" >RIV/61989100:27740/25:10259594 - isvavai.cz</a>
Result on the web
<a href="https://www.nature.com/articles/s41598-025-24067-8" target="_blank" >https://www.nature.com/articles/s41598-025-24067-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1038/s41598-025-24067-8" target="_blank" >10.1038/s41598-025-24067-8</a>
Alternative languages
Result language
angličtina
Original language name
Comparative analysis of lump, breather, and interaction solutions using a bidirectional data mapping approach
Original language description
This study analyzes the (2+1)-dimensional Boussinesq equation, a fundamental model in coastal and ocean engineering for describing the propagation of long waves in shallow water. Understanding the nonlinear wave structures of this equation is essential for predicting energy localization, wave stability, and extreme events such as rogue waves. To this end, the Hirota bilinear method is employed to derive explicit N-soliton solutions, explicitly classifying them into bright and dark types according to parameter criteria. Breather solutions in different planes are constructed using the complex conjugate approach, while the long-wave limit method is applied to obtain first- and second-order lump waves, representing rationally localized structures. Furthermore, four hybrid solutions combining solitons, lumps, and breathers are developed, and their interaction dynamics (e.g. soliton-soliton and soliton-lump collisions) are systematically analyzed. The interactions are shown to be elastic, and all structures retain their identities after collision. A novel contribution of this work is the use of a bidirectional scatter plot technique to compare the behaviors of these solutions across parameter ranges, providing a unified framework for identifying conditions under which different solutions exhibit similar dynamics. The results demonstrate several practical insights: for example, lump solutions preserve their localization over time, modeling stable energy concentrations, while soliton-breather interactions capture oscillatory instabilities relevant for predicting extreme wave events. These contributions extend beyond previous studies by offering both a systematic taxonomy of nonlinear wave structures and a diagnostic tool for engineers to evaluate wave interactions under varying oceanic conditions.
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
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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
Scientific Reports
ISSN
2045-2322
e-ISSN
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Volume of the periodical
15
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
25
Pages from-to
40242
UT code for WoS article
001618234300043
EID of the result in the Scopus database
2-s2.0-105022140183