Article
Engineering, Mechanical
Yasin Hasanoglu, Cihangir Ozemir
Summary: The study investigates a family of sixth-order Boussinesq equations with arbitrary nonlinearity, examining different types of Lie symmetry algebra and providing exact solutions in the case of quadratic nonlinearity, some of which are expressed in terms of elliptic functions.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Tian-Tian Zhang, Mei-Juan Xu
Summary: A direct and effective method is used to construct discrete models of high-dimensional generalized Zakharov-Kuznetsov and diffusion-convection equations. The potential systems and resulting Lie symmetries are used to derive invariant and symmetry-preserving difference models. Some exact solutions are obtained and verified through graphic analysis.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
S. R. Svirshchevskii
Summary: This paper discusses the problem of finding exact solutions to a nonlinear diffusion equation. By employing substitutions and transformations, explicit solutions of the equation and the dynamics of the solutions on an invariant subspace are obtained.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
Chaudry Masood Khalique, Karabo Plaatjie
Summary: In this article, a two-dimensional generalized shallow water wave equation is investigated by calculating Lie symmetries and performing symmetry reductions. An analytical solution is obtained by utilizing three translation symmetries of the equation, and more closed-form solutions are constructed using Kudryashov's approach. Furthermore, energy and linear momentum conservation laws are computed for the equation by engaging the multiplier approach and Noether's theorem.
Article
Multidisciplinary Sciences
Maria S. Bruzon, Tamara M. Garrido-Letran, Rafael de la Rosa
Summary: This paper discusses a family of generalized Benjamin-Bona-Mahony-Burgers equations, investigating the Lie point symmetries and deriving nonlinear partial differential equations from them. The study also includes the search for exact solutions using Kudryashov's method, determining line soliton solutions in a specific case, and constructing low-order conservation laws through the multipliers method.
Article
Acoustics
Afonso W. Nunes, Samuel da Silva, Adrian Ruiz
Summary: This paper proposes a Lie symmetry method-based approach for systematically computing closed-form general solutions to the mode shape equation of non-uniform and unconventional vibrating rods. The method provides algorithmic order-reduction steps for solving the mode shape equation and obtaining the desired solutions for the problem.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Mathematics, Applied
E. I. Kaptsov, S. V. Meleshko
Summary: The paper analyzes a model of equations of magnetohydrodynamics (MHD) obtained from group classification. The model utilizes Lagrangian coordinates and includes four arbitrary functions. Conservation laws are obtained using Noether's theorem and exact solutions are obtained through explicit or numerical methods.
STUDIES IN APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Adrian Ruiz Servan, Maria Concepcion Muriel Patino
Summary: Variational lambda-symmetries are used to find exact solutions to second- and fourth-order Euler-Lagrange equations associated with variational problems. This approach is particularly useful when standard procedures fail. The paper presents two examples, one involving a first-order variational problem and the other a fourth-order equation, where families of exact solutions are obtained using the variational lambda-symmetry method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Almudena P. Marquez, Maria S. Bruzon
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
Mathematics, Interdisciplinary Applications
Dig Vijay Tanwar
Summary: In this study, symmetry reductions of the Date-Jimbo-Kashiwara-Miwa equation were derived using the Lie symmetry method, resulting in exact solutions that are more generalized than previous results. The physical significance of these solutions was analyzed through numerical simulations.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Bin Hong, Xue-Ling Mu
Summary: This study examines the effects of relativistic parameter sets established at saturation density on the tidal deformabilities and f-mode oscillations of neutron stars. The findings indicate that the isovector saturation parameters have a greater impact than the isoscalar saturation parameters. The study also observes a linear correlation between f-mode frequencies and saturation properties.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2022)
Article
Physics, Mathematical
S. Saha Ray
Summary: This paper explores the integrability, symmetry analysis, group invariant solutions and conservation laws of the Mikhailov-Novikov-Wang equation. Painleve analysis and Lie group analysis methods are employed to study the properties of this equation, leading to the derivation of explicit exact solutions through similarity reduction. Additionally, conservation laws are constructed using a new theorem proposed by Ibragimov.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2021)
Article
Astronomy & Astrophysics
Raj Kishor Joshi, Indranil Chattopadhyay, Dongsu Ryu, Lallan Yadav
Summary: This study focuses on the evolution of one-dimensional relativistic jets using the exact solution of the Riemann problem for relativistic flows. The composition of the jet and ambient medium significantly affects the jet solution, with jet propagation speed depending on the composition and being maximum for a pair-dominated jet. The propagation direction of the reverse-shock may also strongly depend on the composition of the jet.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2021)
Article
Physics, Multidisciplinary
Shitesh Shukla, Mukesh Kumar, Raj Kumar
Summary: The article focuses on the cgKP equation, which describes water waves propagating in straits or rivers, and provides analytical solutions through the generation of Lie symmetries. These solutions demonstrate transitions from double solitons to single solitons and from negatons to positons, reflecting the complex nature of the nonlinear system.
Article
Materials Science, Multidisciplinary
Tukur A. Sulaiman, Abdullahi Yusuf, Fairouz Tchier, Mustafa Inc, F. M. O. Tawfiq, F. Bousbahi
Summary: In this work, the Lie-Backlund symmetry generators and corresponding conservation laws for the general Boussinesq equation are studied using a new conservation theorem and symmetry analysis method. Some important soliton solutions for the equation are constructed by means of two effective analytical schemes, and the physical features of these solutions are plotted to provide a clear outlook.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
K. S. Govinder
Summary: In this paper, symmetry methods are applied to modified Painleve-Ince type equations, and the results are used to indicate the equivalence and solvability of certain equations. The use of Noether symmetries in the reduction of equations is also discussed, and the factorization approach is shown to yield interesting results.
RICERCHE DI MATEMATICA
(2022)
Article
Physics, Particles & Fields
Noeleen Naidoo, Sunil D. Maharaj, Keshlan S. Govinder
Summary: The relationship between radiating stars and Riccati equations in general relativity is examined, considering a general matter distribution including the electromagnetic field and the cosmological constant. A generalized transformation for describing the gravitational potentials of a spherically symmetric relativistic gravitating fluid is introduced, leading to a new Riccati equation at the surface of the radiating star. Exact solutions satisfying the boundary condition are obtained, and the gravitational potentials are explicitly given. Some consistency conditions are reduced to Bernoulli equations, allowing for exact solutions. It is also shown that reducing the order enables the boundary condition to be expressed as a first order equation using the generalized transformation. Solutions obtained using the generalized transformation also satisfy a linear equation of state.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Review
Engineering, Multidisciplinary
Suliman Jamiel M. Abdalla, Faraimunashe Chirove, Keshlan S. Govinder
Summary: This article conducts a systematic review of mathematical models of the Ebola virus disease, aiming to summarize the current research, identify research gaps, and improve future models by addressing the limitations of existing models.
INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION
(2022)
Article
Physics, Multidisciplinary
Sfundo C. Gumede, Keshlan S. Govinder, Sunil D. Maharaj
Summary: This paper investigates the Emden-Fowler equation for the spherically symmetric shear-free spacetimes with a charged matter distribution. A new first integral is obtained by integrating this equation. The explicit forms of f (x) and g(x) are found in terms of elementary and special functions. This is a new solution to the Einstein-Maxwell equations.
Article
Mathematics, Applied
G. S. Rukanda, K. S. Govinder, J. G. O'Hara
Summary: This paper uses partial differential equations to describe option pricing in an illiquid market and applies Lie symmetry analysis to a model that incorporates the effect of large traders. By reducing the PDEs to ordinary differential equations, group invariant solutions are obtained. These solutions are new to the field and can be used as an alternative to simulations.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Genly Leon, Megandhren Govender, Andronikos Paliathanasis
Summary: In this study, we investigate the temporal equation of radiating stars using three powerful methods for the analysis of nonlinear differential equations. The global dynamics of the given master ordinary differential equation are explored to understand the evolution of solutions under different initial conditions and to examine the existence of asymptotic solutions. Additionally, Lie's theory is applied to reduce the order of the master differential equation and determine an exact similarity solution. It is found that the master equation possesses the Painleve property, allowing for expressions of the analytic solution in terms of a Laurent expansion.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Astronomy & Astrophysics
S. K. Maurya, Ksh Newton Singh, M. Govender, Saibal Ray
Summary: In this work, we model compact objects within the framework of Einstein-Gauss-Bonnet (EGB) gravity using gravitational wave events GW 170817 and GW 190814, as well as observations of neutron stars PSR J1614-2230, PSR J1903 + 6620, and LMC X-4. We also explore the impact of anisotropy by varying the decoupling parameter using the extended gravitational decoupling (EGD) method. Our models, which include strange quark stars with the MIT Bag equation of state, are able to achieve the observed masses and radii of compact objects by adjusting the EGB parameter or the decoupling constant.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2023)
Article
Physics, Multidisciplinary
Noeleen Naidoo, Sunil D. Maharaj, Keshlan S. Govinder
Summary: A model of a radiating star undergoing gravitational collapse is constructed by studying the boundary condition and equation of state. New classes of exact solutions with acceleration, expansion and shear in the presence of the cosmological constant are obtained. The range of the equation of state parameters allows the solution to be interpreted as barotropic matter stars or dark energy stars. The model is physically reasonable and satisfies the energy conditions.
Article
Astronomy & Astrophysics
Bikram Keshari Parida, Shyam Das, Megandhren Govender
Summary: In this paper, the influence of tidal Love numbers on the equation-of-state governing the interior matter distribution of a compact star within the framework of classical general relativity is investigated. The Einstein field equations are solved for an arbitrary equation-of-state parameter by assuming a linear equation-of-state for a spherically symmetric anisotropic matter configuration. The model is subjected to rigorous regularity, causality, and stability tests, and shows a very good approximation of the pulsar 4U 1608-52. The intrinsic connection between the equation-of-state parameter and the tidal Love numbers is further demonstrated.
INTERNATIONAL JOURNAL OF MODERN PHYSICS D
(2023)
Article
Mathematics, Interdisciplinary Applications
Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove
Summary: Spatial heterogeneity and migration of hosts and ticks affect the spread, extinction and persistence of tick-borne diseases. In this paper, we use a stochastic differential equations model to investigate the impact of white-tailed deer and lone star ticks migration on the dynamics of tick-borne diseases. We derive a general formula for computing the basic reproduction number for all patches and show that disease extinction can be increased by controlling or prohibiting the movement of hosts and ticks.
FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS
(2023)
Article
Physics, Particles & Fields
Sunil D. Maharaj, Noeleen Naidoo, Gareth Amery, Keshlan S. Govinder
Summary: The Karmarkar embedding condition in different spherically symmetrical metrics is studied using Lie symmetries. The study extends recent results by investigating the Lie symmetries for conformally flat and shear-free metrics. Additionally, the Lie symmetries for geodesic metrics and general spherical spacetimes are obtained for the first time. The study also demonstrates that the Karmarkar condition can be used to produce an embeddable relativistic radiating star with a barotropic equation of state via Lie symmetries.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Physics, Particles & Fields
Noeleen Naidoo, Sunil D. Maharaj, Keshlan S. Govinder
Summary: The objective of this study is to investigate spherically symmetric radiating stars undergoing gravitational collapse, in higher dimensional general relativity, inclusive of acceleration, expansion, shear, an electromagnetic field and a cosmological constant. Two approaches are studied to obtain exact solutions to the boundary condition with/without a linear equation state. Transformations that map the boundary condition into a new Riccati equation are investigated to obtain new exact models. The importance of these transformations in reducing the order of the boundary condition and obtaining new solutions is shown.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Astronomy & Astrophysics
Sunil Kumar Maurya, Ksh. Newton Singh, Megandhren Govender, Ghulam Mustafa, Saibal Ray
Summary: Inspired by the gravitational event GW190814, this study models compact objects within the framework of f(Q) gravity using the method of gravitational decoupling. The findings reveal that the quadratic equation of state (EOS) is the most suitable and versatile model, capable of describing various compact objects, including neutron stars and the secondary component of GW190814.
ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES
(2023)
Article
Physics, Particles & Fields
S. K. Maurya, M. Govender, G. Mustafa, Riju Nag
Summary: In this work, the Karmarkar condition and the concept of vanishing complexity are employed to generate models of compact stars within the framework of complete geometric deformation. Anisotropic pressure plays a key role in determining the stability of compact objects, while the magnitude of the decoupling constant determines the direction of energy flow.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Astronomy & Astrophysics
Sudan Hansraj, Megandhren Govender, Lushen Moodly, Ksh Newton Singh
Summary: We study the influence of higher curvature effects on stellar structure and find that the properties of stars are greatly affected when these terms are dynamic. By constructing a model of a superdense star with a strange star equation of state, we discover that the higher curvature terms reduce the speed of sound and significantly decrease the values of the surface gravitational redshift compared to general relativity. These findings have important implications for interpreting observations in relativistic astrophysics.
