Article
Mathematics, Applied
Andronikos Paliathanasis, Genly Leon, P. G. L. Leach
Summary: In this article, we revise recent results on the classification of the generalized three-dimensional Hamiltonian Ermakov system. We correct a recently published statement and provide a complete solution for the classification problem. Furthermore, we extend our results to the generalized n-dimensional Hamiltonian Ermakov system.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Matteo Gorgone, Francesco Oliveri
Summary: This paper discusses approximate Noether symmetries of variational problems involving small terms within the framework of the consistent approach for approximate Lie symmetries of differential equations. An approximate Noether theorem is proposed to construct approximate conservation laws, with illustrative applications provided.
Article
Mathematics
Umara Kausar, Tooba Feroze
Summary: The paper investigates the method of finding approximate Mei symmetries and invariants, presenting the results in the form of theorems and proofs, with a simple example in mechanics for illustration. A comparison between approximate Mei symmetries and Noether symmetries reveals that there is only one common symmetry between the two sets.
Article
Mechanics
Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman Kozlov, Sergey Meleshko
Summary: This paper investigates symmetries and conservation laws in the mass Lagrangian coordinates of one-dimensional magnetohydrodynamics flows. It analyzes flows with cylindrical symmetry and assumes the medium to be inviscid and thermally non-conducting, modeled by a polytropic gas. The study identifies additional symmetries in cases of finite electric conductivity and presents conservation laws through direct computation. For cases with infinite electric conductivity, the study considers variational formulations and uses the Noether theorem to compute conservation laws.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2023)
Article
Mechanics
Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman Kozlov, Sergey Meleshko, Potcharapol Mukdasanit
Summary: This paper considers the one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The symmetries, conservation laws, and variational form are examined for both finite and infinite electric conductivity cases. Lie group classification and direct computation are used to establish symmetry extensions and derive conservation laws. By utilizing the variational structure and Noether theorem, conservation laws are obtained in physical variables.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2022)
Article
Physics, Multidisciplinary
R. Mohanasubha, V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan
Summary: In this work, a new approach is presented to find non-local symmetries and contact symmetries from the admitted Lie point symmetries of a system of nonlinear differential equations. By introducing a new function in the relation between the lambda-symmetry function and the Lie point symmetry characteristics, both non-local symmetries and contact symmetries are generated. The results are validated using examples such as the Ricatti chain and the Mathews-Lakshmanan oscillator equation where the contact symmetries are identified.
PRAMANA-JOURNAL OF PHYSICS
(2023)
Article
Physics, Particles & Fields
L. K. Duchaniya, Santosh Lohakare, B. Mishra, S. K. Tripathy
Summary: In this paper, the stability analysis of accelerating cosmological models obtained in f(T) gravity theory is emphasized. The phantom-like behavior of the models at the present epoch is observed based on the evolution of the equation of state parameter. Perturbation technique and dynamical system analysis are used to demonstrate the stability and critical points of the models. In each of the two specific f(T) gravity models, at least one stable critical point is observed.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Mathematics, Applied
Andronikos Paliathanasis
Summary: This study focuses on the group properties of shallow-water equations with complete Coriolis force, using Lie theory to classify the system and derive new similarity solutions based on admitted Lie point symmetries.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(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
Astronomy & Astrophysics
Sourav Dutta, Muthusamy Lakshmanan, Subenoy Chakraborty
Summary: In this study, quantum cosmology with quintom dark energy model was investigated through symmetry analysis of the underlying physical system. The study focused on the flat FLRW model and utilized Noether symmetry to obtain an appropriate conserved charge. The Wheeler-DeWitt equation was then constructed on the minisuperspace to obtain solutions using the conserved charge.
PHYSICS OF THE DARK UNIVERSE
(2021)
Article
Engineering, Electrical & Electronic
Syed T. R. Rizvi, Aly R. Seadawy, Azhar Bashir, Nimra
Summary: In this paper, we perform a Lie symmetry analysis on the nonlinear equation describing chains of atoms with long range interaction. We calculate the conserved density and associated fluxes using the scaling invariance approach and employ the Euler and homotopy operators. Additionally, we use a sub-ODE scheme to obtain various solitary wave solutions with certain constraints. Finally, we present the graphical results in different dimensions.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Astronomy & Astrophysics
Adriano Acunzo, Francesco Bajardi, Salvatore Capozziello
Summary: This article discusses extensions of General Relativity based on the non-local function f(R, rectangle(-1) R) and explores the role of non-locality in cosmology. Viable exact solutions are found by selecting viable models using the Noether Symmetry Approach.
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Physics, Particles & Fields
Carlos E. Yaguna, Oscar Zapata
Summary: In multi-component scalar dark matter scenarios, a single Z(N) symmetry is studied for the stability of different dark matter particles, with two species contributing to the observed dark matter density. The analysis of three scenarios shows that new interactions allowed by the Z(2n) symmetry can satisfy current experimental constraints over a wider range of dark matter masses and may lead to observable signals in direct detection experiments. These scenarios can serve as prototypes for other two-component Z(2n) models with one complex and one real dark matter particle.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Mathematics
Andronikos Paliathanasis, Genly Leon, Peter G. L. Leach
Summary: The Lie symmetry analysis is applied to the 1 + n fourth-order Schrodinger equation inspired by the modification of the deformation algebra with a minimum length. The potential function of the scalar field is classified and the equation is simplified. A qualitative analysis is conducted to understand the asymptotic dynamics.
Article
Engineering, Multidisciplinary
Andronikos Paliathanasis
Summary: We apply Lie theory to determine the infinitesimal generators of point transformations that leave the 3 + 1 Kudryashov-Sinelshchikov equation invariant. We classify the one-dimensional optimal system and derive all possible independent Lie invariants. The existence of travel-wave solutions is proven using the results, and singularity analysis shows that the equation possesses the Painleve property and solutions can be written using a Laurent expansion.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Andronikos Paliathanasis
Summary: In this study, we analyze the group properties of a recently proposed 2+1 extended Boiti-Leon-Manna-Pempinelli equation using the theory of Lie symmetries. We find that the equation possesses an infinite number of Lie symmetries, leading to an infinite number of solutions. By applying Lie invariants, we obtain D'Alembert-type wave solutions and identify new periodic solutions.
QUAESTIONES MATHEMATICAE
(2023)
Article
Engineering, Multidisciplinary
Andronikos Paliathanasis
Summary: This paper presents a symmetry classification study of the hyperbolic system of partial differential equations describing a drift-flux two-phase flow in a one-dimensional pipe. The results show that the fluid equations are invariant under the elements of a three-dimensional Lie algebra for general polytropic indices, but additional Lie point symmetries occur for specific values of the polytropic indices. The one-dimensional systems are investigated in each case, with similarity transformations used to reduce the fluid equations into a system of ordinary differential equations. Exact solutions are derived and the reduced systems are studied numerically.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Andronikos Paliathanasis, Genly Leon
Summary: We investigate exact solutions and the asymptotic dynamics for the Friedmann-Lemaitre-Robertson-Walker universe with nonzero spatial curvature in the fourth-order modified teleparallel gravitational theory known as f(T,B) theory. The field equations can be described in minisuperspace and can reproduce any exact form of the scale factor. Equilibrium points are calculated and their stability is analyzed. Milne and Milne-like solutions are supported, and the existence of a de Sitter universe is shown. Poincare variables are used to investigate the dynamics at infinity in order to complete the analysis.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Multidisciplinary Sciences
Andronikos Paliathanasis
Summary: We conducted a detailed study on the potential classification of the Klein-Gordon equation in anisotropic Riemannian manifolds. Specifically, we focused on the Klein-Gordon equations in four-dimensional anisotropic and homogeneous spacetimes of Bianchi I, Bianchi III, and Bianchi V. By deriving closed-form expressions for the potential function, we were able to find the Lie and Noether symmetries of the equations. Applying previous results connecting the Lie symmetries with the collineations of the Riemannian space, we systematically solved the classification problem.
Article
Mathematics
Genly Leon, Alfredo D. Millano, Andronikos Paliathanasis
Summary: In this study, we investigate the phase space of a scalar field theory obtained through minisuperspace deformation. We consider quintessence or phantom scalar fields in the action derived from minisuperspace deformation on the Einstein-Hilbert action. Our analysis utilizes a modified Poisson algebra with alpha-deformed Poisson brackets that are linked to the Moyal-Weyl star product. We discuss both early- and late-time attractors and reconstruct the cosmological evolution. Additionally, we demonstrate that the model can exhibit the lambda CDM model as a future attractor if we start with a massless scalar field without a cosmological constant term.
Article
Mathematics
Andronikos Paliathanasis, Peter G. L. Leach
Summary: We extend our analysis on the Lie symmetries in fluid dynamics to macroscopic traffic estimation models. Specifically, we study the Aw-Rascle-Zhang model, which consists of two hyperbolic first-order partial differential equations. We determine the Lie symmetries, the one-dimensional optimal system, and the corresponding Lie invariants. We find that the admitted Lie symmetries form the four-dimensional Lie algebra A(4,12). The resulting one-dimensional optimal system is composed of seven one-dimensional Lie algebras. We use the Lie symmetries to define similarity transformations and derive new analytic solutions for the traffic model, discussing the qualitative behavior of the solutions.
Article
Physics, Multidisciplinary
Andronikos Paliathanasis
Summary: A detailed analysis is presented on the phase-space for the field equations in scalar field cosmology with a chameleon cosmology. Four different sets of potential and coupling function are considered. The H-normalization approach and dimensionless variables are used to analyze the field equations. The asymptotic solutions describe the main eras of cosmological history and the existence of acceleration solutions. The Chameleon dark energy model is concluded to be a unified model for the dark sector of the universe.
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Andronikos Paliathanasis
Summary: The Lie symmetry analysis is applied to a modified one-dimensional Saint-Venant system with density dependent on fluid temperature. The system includes a plane bottom geometry, non-zero viscosity term, and gravitational force. The resulting Lie symmetries form a four-dimensional Lie algebra, A(3,3) circle plus A(1), while for the viscosity free model, the symmetries form a six-dimensional A(5,19) circle plus A(1) algebra. Optimal systems and independent reductions are determined for each algebra, leading to new exact and analytic solutions for the modified Saint-Venant system.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Bayron Micolta-Riascos, Alfredo D. Millano, Genly Leon, Cristian Erices, Andronikos Paliathanasis
Summary: Recently, researchers have been using fractional calculus to address cosmological problems by altering the gravitational action integral, comparing the resulting theory with observational data. By studying the phase spaces for different fractional order derivatives and matter contents, equilibrium points can be classified, providing a range for investigating cosmological history and obtaining an accelerating power-law solution for the scale factor. This paper discusses the physical interpretation of these cosmological solutions and emphasizes the influence of fractional derivatives in a theory of gravity with a scalar field.
FRACTAL AND FRACTIONAL
(2023)
Editorial Material
Physics, Nuclear
Andronikos Paliathanasis
Summary: This paper reviews the Noether symmetry analysis for Chameleon cosmology presented in R. Bhaumik, S. Dutta and S. Chakraborty, Int. J. Mod. Phys. A 37, 2250018 (2022). It shows that the classification problem for the field equations in Chameleon cosmology is still open.
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
(2023)
Article
Astronomy & Astrophysics
Andronikos Paliathanasis
Summary: This study analyzes the phase-space of an alternate scalar field cosmology that combines the concepts of dark energy and the dark sector. The findings indicate that a de Sitter universe can only be achieved when the potential function is constant. The presence of a de Sitter universe depends on the functional form of the potential function, with a finite regime for a constant potential and an infinite regime for an exponential potential. The cosmological viability of the theory is discussed.
Article
Multidisciplinary Sciences
Andronikos Paliathanasis
Summary: A detailed symmetry analysis is conducted for a microscopic model of traffic flow in two-lane motorways. The model is an extension of the Aw-Rascle theory and describes flow parameters using first-order partial differential equations. The model is expressed in terms of Euler and Lagrange variables, and different Lie algebras and optimal systems are found for each variable set. The Lie symmetries are then used to derive new closed-form solutions.
Article
Astronomy & Astrophysics
Andronikos Paliathanasis, P. G. L. Leach
Summary: We provide a complete algebraic classification of the Lie symmetries for generalized Zoomeron equations. For the generalized 1 + 1 and 2 + 1 Zoomeron equations, we solve the Lie symmetry conditions to constrain the free functions. It is found that the considered differential equations have the same number of Lie symmetries as the non-generalized equations. The admitted Lie symmetries form different Lie algebras for the two cases. A one-dimensional optimal system is constructed and similarity solutions are derived, leading to kink solutions.
MODERN PHYSICS LETTERS A
(2023)
Article
Astronomy & Astrophysics
Andronikos Paliathanasis
Summary: We apply Noether symmetries to constrain the unknown functions in chameleon gravity in the cosmological scenario. We find new analytic solutions by constructing conservation laws and without assuming the presence of a pressureless fluid. The analysis shows that these solutions can reproduce the ΛCDM model in the late universe.
PHYSICS OF THE DARK UNIVERSE
(2023)