Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory

Hassan Almusawa () and Adil Jhangeer ()
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Hassan Almusawa: Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia
Adil Jhangeer: IT4Innovations, VSB—Technical University of Ostrava, Poruba, 708 00 Ostrava, Czech Republic

Mathematics, 2024, vol. 12, issue 14, 1-12

Abstract: This study introduces the KdV–Caudrey–Dodd–Gibbon (KdV-CDGE) equation to describe long water waves, acoustic waves, plasma waves, and nonlinear optics. Employing a generalized new auxiliary equation scheme, we derive exact analytical wave solutions, revealing rational, exponential, trigonometric, and hyperbolic trigonometric structures. The model also produces periodic, dark, bright, singular, and other soliton wave profiles. We compute classical and translational symmetries to develop abelian algebra, and visualize our results using selected parameters.

Keywords: mathematical model; visualization; Lie theory; abelian algebra; identification of essential parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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