Mathematics And Statistics - Research Publications

Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47

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Author: search.filters.author.Gupta, Rajesh Kumar

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    Optical soliton solutions of the conformable time fractional Radhakrishnan�Kundu�Lakshmanan Model
    (Springer, 2022-09-13T00:00:00) Yadav, Vikash; Gupta, Rajesh Kumar
    In the present study, we have obtained different kinds of wave solutions which possess distinctive physical characteristics of the nonlinear conformable time fractional Radhakrishnan�Kundu�Lakshmanan model by utilizing the generalized Jacobi elliptic function method. 3-D surfaces to some of the reported solutions are plotted and the dependence of the behaviour of the solutions on the fractional derivative has also been analyzed in the present study. In addition to providing physical explanation of Radhakrishnan-Kundu-Lakshmanan equation, the solutions presented here may also provide an insight into the study of wave propagation in various conformable fractional nonlinear models arising in nonlinear sciences. � 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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    Symmetry reduction, conservation laws and power series solution of time-fractional variable coefficient Caudrey�Dodd�Gibbon�Sawada�Kotera equation
    (Springer Medizin, 2021-10-13T00:00:00) Manjeet; Gupta, Rajesh Kumar
    In this paper, Lie classical approach is utilized for the symmetry reduction of time-fractional variable coefficient Caudrey�Dodd�Gibbon�Sawada�Kotera equation. The obtained symmetries and Erde� lyi�Kober fractional differential operator are used to reduce the original nonlinear partial differential equation into nonlinear ordinary differential equation. The generalized Noether operator and new conservation theorem are exploited to obtain conservation laws of the governing equation. The power series solution is also derived for the considered equation. The obtained power series solution is investigated for the convergence and the obtained power series solution is convergent. � 2021, The Author(s), under exclusive licence to Islamic Azad University.
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    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.
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    A note on optimal systems of certain low-dimensional Lie algebras
    (De Gruyter Open Ltd, 2020-12-22T00:00:00) Singh, Manjit; Gupta, Rajesh Kumar
    Optimal classifications of Lie algebras of some well-known equations under their group of inner automorphism are re-considered. By writing vector fields of some known Lie algebras in the abstract format, we have proved that there exist explicit isomorphism between Lie algebras and sub-algebras which have already been classified. The isomorphism between Lie algebras is useful in the sense that the classifications of sub-algebras of dimension ?4 have previously been carried out in literature. These already available classifications can be used to write classification of any Lie algebra of dimension ?4. As an example, the explicit isomorphism between Lie algebra of variant Boussinesq system and sub-algebra A 3,5 1 / 2 ${A}_{3,5}^{1/2}$ is proved, and subsequently, optimal sub-algebras up to dimension four are obtained. Besides this, some other examples of Lie algebras are also considered for explicit isomorphism. � 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.