M. C. Nucci, “Jacobi's last multiplier, Lie symmetries, and hidden linearity: "Goldfishes" galore”, TMF, 151:3 (2007), 495–509; Theoret. and Math. Phys., 151:3 (2007), 851

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 3, Pages 495–509
DOI: https://doi.org/10.4213/tmf6062 (Mi tmf6062)

This article is cited in 16 scientific papers (total in 16 papers)

Jacobi's last multiplier, Lie symmetries, and hidden linearity: "Goldfishes" galore

M. C. Nucci

Università degli Studi di Perugia

Full-text PDF (448 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf6062

Abstract: In addition to the reduction method, we present a novel application of Jacobi's last multiplier for finding Lie symmetries of ordinary differential equations algorithmically. These methods and Lie symmetries allow unveiling the hidden linearity of certain nonlinear equations that are relevant in physics. We consider the Einstein–Yang–Mills equations and Calogero's many-body problem in the plane as examples.

Keywords: Lie group analysis, first integral, Jacobi's last multiplier.

English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 3, Pages 851–862
DOI: https://doi.org/10.1007/s11232-007-0070-8

Bibliographic databases:

Language: Russian

Citation: M. C. Nucci, “Jacobi's last multiplier, Lie symmetries, and hidden linearity: "Goldfishes" galore”, TMF, 151:3 (2007), 495–509; Theoret. and Math. Phys., 151:3 (2007), 851–862

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https://doi.org/10.4213/tmf6062

https://www.mathnet.ru/eng/tmf/v151/i3/p495

This publication is cited in the following 16 articles:

Andronikos Paliathanasis, “Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization”, Axioms, 13:5 (2024), 331
Mohanasubha Ramasamy, Subhasri Devarajan, Senthilvelan Murugaian, Karthikeyan Rajagopal, “On exploring $\lambda$ -symmetries, Darboux polynomials and other integrable quantifiers of Easter Island Population Model”, Pramana - J Phys, 97:3 (2023)
Paliathanasis A., “Lie Symmetries and Similarity Solutions For a Family of 1+1 Fifth-Order Partial Differential Equations”, Quaest. Math., 45:7 (2022), 1099–1114
Paliathanasis A., “One-Dimensional Optimal System and Similarity Transformations For the 3+1 Kudryashov-Sinelshchikov Equation”, Int. J. Nonlinear Sci. Numer. Simul., 2021
Luo Sh.-K., Zhang X.-T., He J.-M., “A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications”, Acta Mech., 228:1 (2017), 157–174
Gambino G., Tanriver U., Guha P., Choudhury A.G., Choudhury S.R., “Regular and Singular Pulse and Front Solutions and Possible Isochronous Behavior in the Short-Pulse Equation: Phase-Plane, Multi-Infinite Series and Variational Approaches”, Commun. Nonlinear Sci. Numer. Simul., 20:2 (2015), 375–388
Tanriver U., Choudhury S.R., Gambino G., “Lagrangian Dynamics and Possible Isochronous Behavior in Several Classes of Non-Linear Second Order Oscillators Via the Use of Jacobi Last Multiplier”, Int. J. Non-Linear Mech., 74 (2015), 100–107
Nucci M.C., “Symmetries for Thought”, Miskolc Math. Notes, 14:2 (2013), 461–474
Nucci M.C., “Many conserved quantities induced by Lie symmetries of a Lagrangian system”, Phys Lett A, 375:11 (2011), 1375–1377
Nucci M.C., Tamizhmani K.M., “Lagrangians for dissipative nonlinear oscillators: the method of Jacobi last multiplier”, J. Nonlinear Math. Phys., 17:2 (2010), 167–178
Nucci M.C., Tamizhmani K.M., “Using an old method of Jacobi to derive Lagrangians: A nonlinear dynamical system with variable coefficients”, Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics in Physics, 125:3 (2010), 255–269
Nucci M.C., Leach P.G.L., “An Old Method of Jacobi to Find Lagrangians”, Journal of Nonlinear Mathematical Physics, 16:4 (2009), 431–441
Nucci MC, Leach PGL, “The Jacobi Last Multiplier and its applications in mechanics”, Physica Scripta, 78:6 (2008), 065011
Nucci MC, Leach PGL, “Jacobi's last multiplier and Lagrangians for multidimensional systems”, Journal of Mathematical Physics, 49:7 (2008), 073517
Nucci, MC, “Lagrangians galore”, Journal of Mathematical Physics, 48:12 (2007), 123510
A. Gradassi, M.C. Nucci, “Hidden linearity in systems for competition with evolution in ecology and finance”, Journal of Mathematical Analysis and Applications, 333:1 (2007), 274

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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