Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation

Popis výsledku v původním jazyce

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 &amp; auml;cklund transformations (BT). The first B &amp; 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 &amp; 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.

Název v anglickém jazyce

Analyzing coupled-wave dynamics: lump, breather, two-wave and three-wave interactions in a (3+1)-dimensional generalized KdV equation

Popis výsledku anglicky

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 &amp; auml;cklund transformations (BT). The first B &amp; 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 &amp; 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.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Dynamics

ISSN

0924-090X

e-ISSN

1573-269X

Svazek periodika

112

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

22323-22341

Kód UT WoS článku

001314169000007

EID výsledku v databázi Scopus

2-s2.0-85203964568