Mathematics And Statistics - Research Publications
Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47
Browse
14 results
Search Results
Item Transmission dynamics of a novel fractional model for the Marburg virus and recommended actions(Springer Science and Business Media Deutschland GmbH, 2023-08-02T00:00:00) Singh, Jaskirat Pal; Abdeljawad, Thabet; Baleanu, Dumitru; Kumar, SachinMarburg virus disease is a particularly virulent illness that causes hemorrhagic fever and has a fatality rate of up to 88%. It belongs to the same family of pathogens as the Ebola virus. The disease was first identified in 1967 as a result of two significant epidemics that happened concurrently in Marburg, hence the name Marburg, Frankfurt, both in Germany, and Belgrade, Serbia. This work proposes a unique fractional model for the Marburg virus based on the Atangana�Baleanu derivative in the Caputo sense. For the model, two equilibrium states have been founded: endemic equilibrium and disease-free equilibrium. If R< 1 , Castillo�s method and the next-generation matrix are used to demonstrate the disease-free equilibrium�s asymptotic global stability. When R> 1 , the endemic equilibrium point is locally asymptotically stable, according to the linearization. The model�s basic reproduction rates for both humans and bats are calculated using the parameter values. Fixed point theory is used to demonstrate the solution�s existence and uniqueness. Number of infected bats should be controlled and interaction with just recovered individuals should be avoided as these are the main contributors in the infection rate. These recommended actions will make the infected persons in the humans disappear, as demonstrated by the model�s numerical simulations. � 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.Item General form of axially symmetric stationary metric: exact solutions and conservation laws in vacuum fields(Institute of Physics, 2023-06-24T00:00:00) Jyoti, Divya; Kumar, SachinThe invariant non-static solutions of Einstein�s vacuum field equations, corresponding to the most general form of axially symmetric stationary line element that represents a non conformally flat semi-Riemannian spacetime in cylindrical coordinates, are investigated. Lie symmetry method is used for symmetry reduction as well as for obtaining exact solutions in terms of arbitrary functions. The conservation laws are obtained for vacuum equations in axially symmetric gravitational fields. The solutions of Lewis metric and Chandrasekhar metric, are derived from the obtained solutions. By considering the possibilities of arbitrary functions, the graphical behaviour of the solutions is also shown. � 2023 IOP Publishing Ltd.Item Highly dispersive W�shaped and other optical solitons with quadratic�cubic nonlinearity: Symmetry analysis and new Kudryashov's method(Elsevier Ltd, 2023-06-24T00:00:00) Yadav, Ravindra; Malik, Sandeep; Kumar, Sachin; Sharma, Rajesh; Biswas, Anjan; Y?ld?r?m, Yakup; Gonz�lez-Gaxiola, O.; Moraru, Luminita; Alghamdi, Abdulah A.Lie symmetry analysis is utilized in this paper to explore the properties of highly dispersive optical solitons that exhibit quadratic�cubic self-phase modulation. The use of Lie symmetry analysis enables the reduction of the governing partial differential equation to an ordinary differential equation, which is then integrated using an enhanced Kudryashov's approach to obtain solitons with the model. The analysis presented in this paper does not explicitly discuss the formation and dynamics of soliton radiation. � 2023Item Application of new Kudryashov method to various nonlinear partial differential equations(Springer, 2022-11-13T00:00:00) Malik, Sandeep; Hashemi, Mir Sajjad; Kumar, Sachin; Rezazadeh, Hadi; Mahmoud, W.; Osman, M.S.The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models. � 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Item Soliton Solutions of�Dual-mode Kawahara Equation via�Lie Symmetry Analysis(Springer Science and Business Media Deutschland GmbH, 2022-06-29T00:00:00) Malik, Sandeep; Kumar, SachinIn this article, we investigate a newly proposed dual-mode Kawahara equation. Our main aim in this paper is to find out the soliton and periodic solutions of the Kawahara equation. Initially, we reduce the governing equation into an ordinary differential equation by applying the Lie symmetry analysis. Further, we derive the soliton and periodic solutions via three integration methods, namely sech-csch scheme, exp-expansion method, and modified F-expansion method. � 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.Item The (3 + 1)-dimensional Benjamin-Ono equation: Painlev� analysis, rogue waves, breather waves and soliton solutions(World Scientific, 2022-06-08T00:00:00) Kumar, Sachin; Malik, SandeepIn this paper, we analyzed the (3 + 1)-dimensional Benjamin-Ono (BO) equation. We first demonstrated that the governing model is not integrable in the Painlev� sense. The rogue wave and the breather wave solutions are then achieved with the use of bilinear form. Furthermore, using a combination of Lie symmetry analysis with the new Kudryshov method, and the Riccati equation technique, the abundant soliton and singular periodic solutions were derived. The criteria for existence of such solutions are also provided. Consequently, the derived solutions are presented graphically through 3D, 2D and contour plots, which describe useful physical phenomena due to existence of the free parameters. Corresponding to the one-reduction, power series solution of BO equation is also obtained. � 2022 World Scientific Publishing Company.Item Soliton solutions of (2+1) and (3+1)-dimensional KdV and mKdV equations(American Institute of Physics Inc., 2022-03-19T00:00:00) Kumar, Sachin; Malik, SandeepIn this paper, we investigate the (2+1) and (3+1)-dimensional Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. Firstly these equations are converted into ordinary differential equations via traveling wave transforma- tions. Then bright and singular soliton solutions are derived via new version of kudryashov method. � 2022 Author(s).Item Doubly periodic wave structure of the modified Schr�dinger equation with fractional temporal evolution(Elsevier B.V., 2022-01-01T00:00:00) Kumari, Pinki; Gupta, R.K.; Kumar, Sachin; Nisar, K.S.Abundant Jacobi elliptic type solutions with distinct physical structures of complex nonlinear conformable time-fractional modified Schr�dinger equation are obtained by using the generalized Jacobi elliptic function (GJEF) method. The Jacobi function expansions may lead to new doubly periodic wave solutions, soliton solutions, and triangular periodic solutions. Nowadays the conformable operator is being used for a better description of the dynamical systems. Motivated by the potential applications of the governed equation in nonlinear optics, biological sciences, and fluid dynamics, these solutions may be significant in the study of wave propagation in the desired field. Symbolic computations are made with the aid of Maple. � 2022 The AuthorsItem Optical solitons and bifurcation analysis in fiber Bragg gratings with Lie symmetry and Kudryashov�s approach(Springer Science and Business Media B.V., 2021-06-24T00:00:00) Malik, Sandeep; Kumar, Sachin; Biswas, Anjan; Ekici, Mehmet; Dakova, Anelia; Alzahrani, Abdullah Khamis; Belic, Milivoj R.A combination of Lie symmetry analysis and Kudryashov�s approach secures optical soliton solutions with fiber Bragg gratings. The bifurcation analysis is carried out, and the phase portrait is presented. � 2021, The Author(s), under exclusive licence to Springer Nature B.V.Item Potential environmental toxicant exposure, metabolizing gene variants and risk of PCOS-A systematic review(Elsevier Inc., 2021-06-11T00:00:00) Sharma, Priya; Bilkhiwal, Nisha; Chaturvedi, Pragya; Kumar, Sachin; Khetarpal, PreetiExposure of environmental toxicants such as potentially toxic metals and pesticides have largely been attributed to produce adverse effects on general women's health and to be more precise on the reproductive system. In order to explore exposure of toxicants and metabolizing gene variants as risk factor for polycystic ovarian syndrome (PCOS), literature search was carried out using the databases PubMed, Central Cochrane Library, Google Scholar, Science Direct with appropriate keywords upto 6 December 2020. While most of the studies indicate higher serum Cu concentration and lower concentration of Mn as risk factor, studies also report presence of higher pesticide concentration in PCOS women. Genes such as MTHFR, CYPs participate in the metabolism of toxicants and may show different response due to underlying genetic variants. Thus, toxicant exposure are to some extent responsible for the pathogenesis of syndrome through oxidative stress and endocrine disruption, but the susceptibility may vary due to the underlying genetic polymorphism of the exposed population. � 2021 Elsevier Inc.