Browsing by Author "Kumar, Sachin"

Now showing 1 - 20 of 23

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, Sandeep
In 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.
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.
The beneficial effect of rice bran extract against rotenone-induced experimental parkinson�s disease in rats
(Bentham Science Publishers, 2021-02-12T00:00:00) Kumar, Sachin; Kumar, Puneet
Background: Neurodegenerative diseases have become an increasing cause of various disabilities worldwide, followed by aging, including Parkinson�s disease (PD). Parkinson�s disease is a degenerative brain disorder distinguished by growing motor & non-motor failure due to the de-generation of medium-sized spiked neurons in the striatum region. Rotenone is often employed to originate the animal model of PD. It is a powerful blocker of mitochondrial complex-I, mitochon-drial electron transport chain that reliably produces Parkinsonism-like symptoms in rats. Rice bran (RB) is very rich in polyunsaturated fatty acids (PUFA) and nutritionally beneficial compounds, such as ?-oryzanol, tocopherols, and tocotrienols and sterols are believed to have favorable out-comes on oxidative stress & mitochondrial function. Objective: The present study has been designed to explore RB extract�s effect against rotenone-in-duced neurotoxicity in rats. Methods: In the present study, Rotenone (2 mg/kg, s.c) was administered systemically for 28 days. The hexane extract of RB was prepared using Soxhlation. Hexane extract (250 & 500 mg/kg) was administered per oral for 28 days in rotenone-treated groups. Behavioral parameters (grip strength, motor coordination, locomotion, and catalepsy) were conducted on the 7th, 14th, 21st, and 28th day. Animals were sacrificed on the 29th day for biochemical estimation in the striatum and cortex. Results: This study demonstrates significant alteration in behavioral parameters, oxidative burden (increased lipid peroxidation, nitrite concentration, and decreased glutathione, catalase, SOD) in rotenone-treated animals. Administration of hexane extract of RB prevented the behavioral, biochemical alterations induced by rotenone. The current research has been sketched to inspect RB ex-tract�s effect against rotenone-developed neurotoxicity in rats. Conclusion: The findings support that PD is associated with impairments in motor activity. The results also suggest that the nutraceutical rice bran that contains ?-oryzanol, Vitamin-E, ferulic acid etc., may underlie the adjuvant susceptibility towards rotenone-induced PD in experimental rats. � 2021 Bentham Science Publishers.
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 Authors
Exact Solutions of Some Complex Non-Linear Equations," Lecture Notes in Engineering and Computer Science
(Newswood Limited, 2018) Kumar, Sachin
Exact solutions of the coupled Higgs and Maccari system are obtained. Travelling wave solutions of coupled Higgs equation and Maccari system in the form of Jacobi’s elliptical functions are presented.
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, Sachin
The 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.
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. � 2023
Invariance analysis, exact solution and conservation laws of (2 + 1) dim fractional kadomtsev-petviashvili (kp) system
(MDPI AG, 2021-03-16T00:00:00) Kumar, Sachin; Kour, Baljinder; Yao, Shao-Wen; Inc, Mustafa; Osman, Mohamed S.
In this work, a Lie group reduction for a (2 + 1) dimensional fractional Kadomtsev-Petviashvili (KP) system is determined by using the Lie symmetry method with Riemann Liouville derivative. After reducing the system into a two-dimensional nonlinear fractional partial differential system (NLFPDEs), the power series (PS) method is applied to obtain the exact solution. Further the obtained power series solution is analyzed for convergence. Then, using the new conservation theorem with a generalized Noether�s operator, the conservation laws of the KP system are obtained. � 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Invariant Analysis for Space�Time Fractional Three-Field Kaup�Boussinesq Equations
(Springer Science and Business Media Deutschland GmbH, 2020-09-30T00:00:00) Kaur, Jaskiran; Kumar Gupta, Rajesh; Kumar, Sachin
Symmetries of the nonlinear fractional�differential equations are an interesting�and important topic. In this paper, space�time fractional three-field Kaup�Boussinesq equations with Riemann�Liouville fractional derivative are studied for invariant analysis. Symmetries are obtained by using classical Lie�s symmetry approach. Using obtained symmetries, the governing equations reduce to system of fractional ordinary differential equations which contains left and right-sided Erde� lyi- Kober (EK) fractional operators. � 2021, Springer Nature Singapore Pte Ltd.
Invariant solutions of Biswas-Milovic equation
(Springer Netherlands, 2017) Kumar, Sachin
The Biswas-Milovic equation in generalized form and with power law nonlinearity is analyzed for Lie symmetries. The classical Lie group method is applied to derive symmetries of this equation, and the ordinary differential equations deduced are further studied; and some exact solutions are obtained. ? 2016, Springer Science+Business Media Dordrecht.
Invariants of Generalized Fifth Order Non-Linear Partial Differential Equation
(IntechOpen, 2018) Kumar, Sachin
The fifth order non-linear partial differential equation in generalized form is analyzed for Lie symmetries. The classical Lie group method is performed to derive similarity variables of this equation and the ordinary differential equations (ODEs) are deduced. These ordinary differential equations are further studied and some exact solutions are obtained.
A malaria model with Caputo-Fabrizio and Atangana-Baleanu derivatives
(World Scientific, 2020-11-02T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Rangaig, Norodin A.; Kumar, Sachin
In this paper, we study two fractional models in the Caputo-Fabrizio sense and Atangana-Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number R0 is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams-Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order ?. � 2021 World Scientific Publishing Company.
Natural Products as an Alternative Therapy for Brain Tumors: From Bench To Bedside
(Springer Singapore, 2022-09-28T00:00:00) Kumar, Sachin; Kumar, Mandeep; Bijalwan, Anjali; Sharma, Shubham; Kumar, Puneet
Incremental elevation in the trends of a brain tumor in recent years accounts for 5% adult population, whereas the number exceeds 70% in the case of children. Evidence reveals an eventual metastasize of 20%-30% of malignant tumors to the brain�s different regions. Compression in the brain tissue and elevated intracranial pressure mediated by benign and malignant tumors contributed to severe consequences like the central nervous system (CNS) damage or even imperil the patient�s life. Despite multiple therapeutic strategies in the market, none of the drugs are fully effective and safe. Strategic advancement indicates chemotherapy as a treatment of choice for critical conditions like brain tumors, but the chemotherapy drugs toxicity is still a major therapeutic hurdle. Plants and their derived natural products are one of the most emerging targets to strike against brain tumors. Analogs of several natural products are already demonstrated as antitumor in nature, and day by day, advancements unfold various other plant and plant derivatives having such antitumor activity. This chapter aims to underline and emphasize the antitumor agents, which can target brain tumors procured from the natural origin such as natural products and their analogs. The available data on different plants and isolated compounds of natural origin used to reduce and arrest brain tumors is also discussed here. � Springer Nature Singapore Pte Ltd. 2022.
A new Painlev� integrable Broer-Kaup system: symmetry analysis, analytic solutions and conservation laws
(Emerald Publishing, 2021-05-05T00:00:00) Kumar, Sachin; Gupta, Rajesh Kumar; Kumari, Pinki
Purpose: This study aims to find the symmetries and conservation laws of a new Painlev� integrable Broer-Kaup (BK) system with variable coefficients. This system is an extension of dispersive long wave equations. As the system is generalized and new, it is essential to explore some of its possible aspects such as conservation laws, symmetries, Painleve integrability, etc. Design/methodology/approach: This paper opted for an exploratory study of a new Painleve integrable BK system with variable coefficients. Some analytic solutions are obtained by Lie classical method. Then the conservation laws are derived by multiplier method. Findings: This paper presents a complete set of point symmetries without any restrictions on choices of coefficients, which subsequently yield analytic solutions of the series and solitary waves. Next, the authors derive every admitted non-trivial conservation law that emerges from multipliers. Research limitations/implications: The authors have found that the considered system is likely to be integrable. So some other aspects such as Lax pair integrability, solitonic behavior and Backlund transformation can be analyzed to check the complete integrability further. Practical implications: The authors develop a time-dependent Painleve integrable long water wave system. The model represents more specific data than the constant system. The authors presented analytic solutions and conservation laws. Originality/value: The new time-dependent Painleve integrable long water wave system features some interesting results on symmetries and conservation laws. � 2021, Emerald Publishing Limited.
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.
An Overview of the Pathophysiological Mechanisms of 3-Nitropropionic Acid (3-NPA) as a Neurotoxin in a Huntington's Disease Model and Its Relevance to Drug Discovery and Development
(Springer, 2023-02-04T00:00:00) Upadhayay, Shubham; Yedke, Narhari Gangaram; Rahi, Vikrant; Singh, Surbhi; Kumar, Sachin; Arora, Anchal; Chandolia, Priyanka; Kaur, Prabhsharan; Kumar, Mandeep; Koshal, Prashant; Jamwal, Sumit; Kumar, Puneet
Animal models are used to better understand the various mechanisms involved in the pathogenesis of diseases and explore potential pathways that will aid in discovering therapeutic targets. 3-Nitropropionic Acid (3-NPA) is a neurotoxin used to induce Huntington's disease (HD)-like symptoms in experimental animals. The 3-NPA is a fungus toxin that impairs the complex II (succinate dehydrogenase) activity of the mitochondria and reduces ATP synthesis, leading to excessive production of free radicals resulting in the degeneration of GABAergic medium spiny neurons (MSNs) in the striatum. This is characterized by motor impairments a key clinical manifestation of HD. 3-NPA has the potential to alter several cellular processes, including mitochondrial functions, oxidative stress, apoptosis, and neuroinflammation mimicking HD-like pathogenic conditions in animals. This review strives to provide a new insight towards the 3-NPA induced molecular dysfunctioning in developing an animal model of HD. Moreover, we summarise several preclinical studies that support the use of the 3-NPA-induced models for drug discovery and development in HD. This review is a collection of various articles that were published from 1977 to 2022 on Pubmed (1639), Web of Science (2139), and Scopus (2681), which are related to the 3-NPA induced animal model. Graphical Abstract: [Figure not available: see fulltext.] � 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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, Preeti
Exposure 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.
Role of vitamins and minerals as immunity boosters in COVID-19
(Springer Science and Business Media Deutschland GmbH, 2021-06-10T00:00:00) Kumar, Puneet; Kumar, Mandeep; Bedi, Onkar; Gupta, Manisha; Kumar, Sachin; Jaiswal, Gagandeep; Rahi, Vikrant; Yedke, Narhari Gangaram; Bijalwan, Anjali; Sharma, Shubham; Jamwal, Sumit
Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) known as coronavirus disease (COVID-19), emerged in Wuhan, China, in December 2019. On March 11, 2020, it was declared a global pandemic. As the world grapples with COVID-19 and the paucity of clinically meaningful therapies, attention has been shifted to modalities that may aid in immune system strengthening. Taking into consideration that the COVID-19 infection strongly affects the immune system via multiple inflammatory responses, pharmaceutical companies are working to develop targeted drugs and vaccines against SARS-CoV-2 COVID-19. A balanced nutritional diet may play an essential role in maintaining general wellbeing by controlling chronic infectious diseases. A balanced diet including vitamin A, B, C, D, E, and K, and some micronutrients such as zinc, sodium, potassium, calcium, chloride, and phosphorus may be beneficial in various infectious diseases. This study aimed to discuss and present recent data regarding the role of vitamins and minerals in the treatment of COVID-19. A deficiency of these vitamins and minerals in the plasma concentration may lead to a reduction in the good performance of the immune system, which is one of the constituents that lead to a poor immune state. This is a narrative review concerning the features of the COVID-19 and data related to the usage of vitamins and minerals as preventive measures to decrease the morbidity and mortality rate in patients with COVID-19. � 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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, Sandeep
In 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).
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, Sachin
In 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.