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

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, a...

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Bibliographic Details
Published in:Nonlinear dynamics 2024-12, Vol.112 (24), p.22323-22341
Main Authors: Raza, Nauman, Jhangeer, Adil, Amjad, Zeeshan, Rani, Beenish, Muhammad, Taseer
Format: Article
Language:English
Subjects:
Automotive Engineering
Breathers
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Exponential functions
Fluid dynamics
Korteweg-Devries equation
Mechanical Engineering
Nonlinear differential equations
Nonlinear dynamics
Nonlinear optics
Parameters
Partial differential equations
Plasma physics
Random waves
Solitary waves
Transformations (mathematics)
Traveling waves
Vibration
Wave interaction
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Summary: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 Bäcklund transformations (BT). The first Bäcklund 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 Bäcklund 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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-024-10199-5