Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255727" target="_blank" >RIV/61989100:27740/24:10255727 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11071-024-10199-5" target="_blank" >https://link.springer.com/article/10.1007/s11071-024-10199-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11071-024-10199-5" target="_blank" >10.1007/s11071-024-10199-5</a>
Alternative languages
Result language
angličtina
Original language name
Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation
Original language description
In this study, we particularly address the generalized (3+1)-dimensional Kortewegde Vries (KdV) problem as one variation of the KdV equation. This equation can be utilized to simulate a wide range of physical events in a variety of domains, such as nonlinear optics, fluid dynamics, plasma physics, and other fields where coupled wave dynamics are significant. We first construct a Hirota bilinear form for the generalized KdV equation, and then we derive two different B & auml;cklund transformations (BT). The first B & auml;cklund transformation includes eleven arbitrary parameters, while the second form contains eight parameters. Rational and exponential traveling wave solutions with random wave numbers are found based on the suggested bilinear B & auml;cklund transformation. These solutions of the rational and exponential functions lead to the formation of dark and bright solitons. Moreover, we utilize the bilinear form of the equation to fully comprehend the behavior of lump-kink, breather, rogue, two-wave, three-wave, and multi-wave solutions. In-depth numerical simulations using 3-D profiles and contour plots are carried out while carefully taking into account relevant parameter values, offering more insights into the unique characteristics of the solutions that are obtained. Our results demonstrate the effectiveness and efficiency of the method used to obtain analytical solutions for nonlinear partial differential equations.
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Dynamics
ISSN
0924-090X
e-ISSN
1573-269X
Volume of the periodical
112
Issue of the periodical within the volume
24
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
22323-22341
UT code for WoS article
001314169000007
EID of the result in the Scopus database
2-s2.0-85203964568