Related references
Note: Only part of the references are listed.
Article
Mathematics, Interdisciplinary Applications
Akhtar Hussain et al.
Summary: This article focuses on the symmetry analysis of the Vakhnenko-Parkes Equation and computes exact solutions using symmetry transformations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Akhtar Hussain et al.
Summary: Nonlinear wave equations in inelastic material are investigated, focusing on a unidirectional nonlinear elastic wave with geometrical nonlinearity. The problem is studied using symmetry method, and an optimal system of non-similar one dimensional subalgebras of Lie algebra is constructed. Symmetry reductions are performed and group invariant solutions are obtained. The problem of nonlinear elastic wave with damping term is also analyzed, and conservation laws of these equations are found using the multiplier approach.
CHINESE JOURNAL OF PHYSICS
(2023)
Article
Physics, Applied
Sibel Tarla et al.
Summary: In this work, we aim to find lump solutions, interaction between lump wave and solitary wave solutions, kink-solitary wave solutions, and shock wave-type solutions to a (3+1)-dimensional generalized nonlinear evolution equation in shallow water waves. By using symbolic computation and Hirota's simple method, we derive the lump solutions, interaction between lump wave and solitary wave solutions, and kink-solitary wave solutions based on a logarithmic derivative transform. These solutions are relevant to natural phenomena like tides, storms, atmospheric currents, and tsunamis. The physical presentation of the solutions is illustrated through 3D and counter graphics with suitable parameter values. We believe that this study can benefit disciplines such as mathematical physics, nonlinear dynamics, fluid mechanics, and engineering sciences.
MODERN PHYSICS LETTERS B
(2023)
Article
Optics
A. Hussain et al.
Article
Materials Science, Multidisciplinary
A. Hussain et al.
Summary: The Lie symmetry analysis is conducted on the RPJ equation in this research. Geometric vector fields are obtained using the classical Lie symmetry technique. A four-dimensional Lie algebra is derived, and a five-dimensional optimal system is obtained based on this algebra. The obtained nonlinear ODEs through similarity reduction are of great significance in understanding the dynamical profile of the solution regions of the RPJ equation. The identified solutions have applications in fluid dynamics and provide insights into recent research due to their association with Reynolds numbers. Mathematica simulations are also provided to understand the physical significance of these solutions.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
M. Usman et al.
Summary: In this research, the system of equations derived from a simplified micromorphic model is studied using the Lie symmetry approach. This approach offers exact invariant solutions, in contrast to the numerical or approximate solutions reported in previous studies. The Lie point symmetries and one-dimensional optimal system of Lie subalgebras are obtained for the model. By using the one-dimensional optimal system, symmetry reductions are performed and corresponding invariant solutions are found. To demonstrate the physical importance of group invariant solutions, 2D, 3D, and contour plots are presented.
RESULTS IN PHYSICS
(2023)
Article
M. Usman et al.
Partial Differential Equations in Applied Mathematics
(2023)
Article
Physics, Multidisciplinary
M. Usman et al.
Summary: This article discusses the thermophoretic motion (TM) equation used to describe soliton-like thermophoresis of wrinkles in Graphene sheet based on the Korteweg-de Vries (KdV) equation. Wrinkle-like exact solutions are constructed using the Lie group method and modified auxiliary equation (MAE) approach. Graphic analysis of the solutions shows how various parameters may change the attributes of the solutions, such as breadth, amplitude, shape, and open direction.
Article
Physics, Multidisciplinary
A. Hussain et al.
Summary: This study focuses on the Lonngren-wave equation (LW Equation) and applies the Lie group analysis to obtain novel solutions. By varying the parameters, the solutions exhibit various wave-like properties, which are further explored through Mathematica simulations to understand the physical dynamics of the model.
CHINESE JOURNAL OF PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
M. Usman et al.
Summary: We obtained new exact waveform solutions for the coupled Drinfeld Sokolov Wilson (DSW) system using the Lie symmetry technique. This system is relevant to various fields such as water waves, theoretical physics, fluid dynamics, biology, and chemical sciences. By using the Jacobi elliptic function (JEF) method, we discovered rational, exponential, and hyperbolic functions based waveform solutions during the symmetry reductions. These solutions exhibit properties of periodic waves, solitary waves, double periodic waves, and shock wave solutions. Some of the solutions found are novel and significant for researchers. Graphical validation of selected solutions was conducted by assigning specific parameter values. This method has potential applications for handling different types of nonlinear evolution systems.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
A. Hussain et al.
Summary: In this paper, the Noether approach is introduced to analyze the Peyrard-Bishop (PB) DNA dynamic model equation. Using the Jacobi elliptic function expansion (JEFE) method, hyperbolic, trigonometric, and rational soliton solutions are obtained. The obtained solutions exhibit properties of shock waves, periodic waves, solitary waves, double periodic waves, and rational solutions. Wolfram Mathematica simulations are used to investigate the wave behaviors.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Multidisciplinary
A. Hussain et al.
Alexandria Engineering Journal
(2023)
Article
Akhtar Hussain et al.
International Journal of Applied and Computational Mathematics
(2023)
Article
Multidisciplinary Sciences
A. Hussain et al.
Summary: In this research, the integrability properties of the S-KdV equation are investigated using Lie symmetry analysis, the modified auxiliary equation method, and the generalized Jacobi elliptic function expansion method. The obtained analytical solutions have a wide range of applications in mathematical physics.
SCIENTIFIC REPORTS
(2023)
Article
Engineering, Mechanical
Long-Xing Li
Summary: A (3+1)-dimensional generalized shallow water waves equation is investigated using different methods. N-soliton solutions, T-breathers, rogue waves, and M-lump solutions are derived through degeneration and parameter limit methods. Furthermore, hybrid solutions composed of soliton, breather, and lump are found during the partial degeneration process of N-soliton.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Dipankar Kumar et al.
Summary: This study presents lump and interaction solutions for the (3+1)-dimensional generalized shallow water equation using the Hirota bilinear method, including multi-stripe and breather wave solutions. The dynamical behaviors of the obtained solutions and the physical interpretation of fission-fusion dynamics are illustrated through graphs. Furthermore, the process of fission-fusion interaction and the characteristics of multi-stripe and breather wave solutions are investigated in detail.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Engineering, Mechanical
Fei-Yan Liu et al.
Summary: In this paper, a (3+1)-dimensional generalized nonlinear evolution equation for shallow water waves is investigated. Nth-order solutions are proved to exist and soliton solutions are constructed. One-periodic-wave solutions are also derived, and the relationship between these solutions is explored. The equation is further simplified to a two-dimensional dynamic system, and the phase portraits of the system are given based on a qualitative analysis.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Sudhir Singh et al.
Summary: In this paper, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform Painleve analysis to understand its integrability nature. We construct higher-order rogue wave solutions using Hirota's bilinearization and generalized polynomial functions, and explore their dynamics in detail, demonstrating potential advantages with available arbitrary constants in their manipulation mechanism.
Article
Physics, Multidisciplinary
Usman Younas et al.
Summary: In this article, the wave behavior of a (3+1)-dimensional dynamical nonlinear model that models shallow water waves is discussed. The Hirota bilinear method is employed to secure the diversity of wave structures, and various types of solutions are extracted. The findings of this research enhance the understanding of nonlinear dynamical behavior and demonstrate the efficacy of the employed methodology.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Yuan Shen et al.
Summary: Researchers investigated water waves and proposed a nonlinear evolution equation, along with soliton solutions. The results depend on the water-wave coefficients in the equation.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics
Almudena P. Marquez et al.
Summary: This paper investigates a one-dimensional non-linear viscoelastic wave equation with non-linear damping and source terms using Lie group theory. By applying Lie symmetries method, the equation is classified and reduced to ordinary differential equations to find new analytical solutions. Low-order conservation laws are derived based on the form of damping and source terms, with discussions on their physical significance.
Article
Engineering, Multidisciplinary
T. S. Moretlo et al.
Summary: Lie symmetry analysis was performed on the integrable Kadomtsev-Petviashvili (TKP) equation, which describes the propagation of two different wave modes simultaneously in the same direction. Similarity reductions and an exact solution were computed, and conservation laws for the underlying equation were derived.
JOURNAL OF APPLIED NONLINEAR DYNAMICS
(2021)
Article
Multidisciplinary Sciences
Tshepo E. Mogorosi et al.
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
(2019)
Article
Engineering, Mechanical
Abdul-Majid Wazwaz et al.
NONLINEAR DYNAMICS
(2019)
Article
Mathematics, Applied
Nail H. Ibragimov
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2007)
