Nonlinear Dynamics and Complex Phenomena in Fluid Mechanics and Related Systems

A special issue of AppliedMath (ISSN 2673-9909).

Deadline for manuscript submissions: 31 March 2026 | Viewed by 276

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Material Sciences, Innovation and Modelling Research Focus Area, Department of Mathematics and Applied Mathematics, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
Interests: nonlinear differential equations; Lie symmetry method; closed-form solutions; conservation laws; mathematical physics; analytical solution methods
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Special Issue Information

Dear Colleagues,

Nonlinear phenomena are common in natural and engineered systems, particularly in the field of fluid mechanics. Nonlinear dynamics often give rise to unexpected outcomes, which presents challenges and chances for innovation. Understanding these behaviours is important for forecasting, controlling, and optimizing these systems. Nonlinear systems are modelled by differential equations that are nonlinear. There is no systematic method that can solve nonlinear differential equations, although various special methods have been developed by researchers in this regard.

This Special Issue seeks to showcase original research focused on nonlinear problems arising in real-world applications, emphasizing innovative numerical, analytical, and experimental methodologies.

Prof. Dr. Chaudry Masood Khalique
Guest Editor

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Keywords

  • nonlinear waves
  • chaos
  • turbulence
  • bifurcation
  • solitons
  • instabilities
  • pattern formation

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Published Papers (1 paper)

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Research

17 pages, 438 KiB  
Article
Analytic Solutions and Conservation Laws of a 2D Generalized Fifth-Order KdV Equation with Power Law Nonlinearity Describing Motions in Shallow Water Under a Gravity Field of Long Waves
by Chaudry Masood Khalique and Boikanyo Pretty Sebogodi
AppliedMath 2025, 5(3), 96; https://doi.org/10.3390/appliedmath5030096 - 31 Jul 2025
Viewed by 141
Abstract
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly [...] Read more.
The Korteweg–de Vries (KdV) equation is a nonlinear evolution equation that reflects a wide variety of dispersive wave occurrences with limited amplitude. It has also been used to describe a range of major physical phenomena, such as shallow water waves that interact weakly and nonlinearly, acoustic waves on a crystal lattice, lengthy internal waves in density-graded oceans, and ion acoustic waves in plasma. The KdV equation is one of the most well-known soliton models, and it provides a good platform for further research into other equations. The KdV equation has several forms. The aim of this study is to introduce and investigate a (2+1)-dimensional generalized fifth-order KdV equation with power law nonlinearity (gFKdVp). The research methodology employed is the Lie group analysis. Using the point symmetries of the gFKdVp equation, we transform this equation into several nonlinear ordinary differential equations (ODEs), which we solve by employing different strategies that include Kudryashov’s method, the (G/G) expansion method, and the power series expansion method. To demonstrate the physical behavior of the equation, 3D, density, and 2D graphs of the obtained solutions are presented. Finally, utilizing the multiplier technique and Ibragimov’s method, we derive conserved vectors of the gFKdVp equation. These include the conservation of energy and momentum. Thus, the major conclusion of the study is that analytic solutions and conservation laws of the gFKdVp equation are determined. Full article
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