Generalized Emden–Fowler equations in noncentral curl forces and first integrals
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DOI: 10.1007/s00707-019-02602-9
Abstract: Noncentral force is an exemplary example of curl force and in general this is not an integrable system. The purpose of this note is twofold. First, we study a different reduction in the noncentral force… read more here.
Keywords: fowler; first integrals; generalized emden; fowler equations ... See more keywords
On the Complete Integrability of the Raychaudhuri Differential System in $$\mathbb {R}^4$$R4 and of a CRNT Model in $$\mathbb {R}^5$$R5
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DOI: 10.1007/s12346-017-0230-7
Abstract: We study the Darboux integrability of two differential systems with parameters: the Raychaudhuri equation (a relativistic model in $$\mathbb {R}^4$$R4) and a chemical reaction model in $$\mathbb {R}^5$$R5. We prove that the first one is… read more here.
Keywords: model mathbb; first integrals; complete integrability; model ... See more keywords
First integrals and general solution of the Fokas–Lenells equation
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DOI: 10.1016/j.ijleo.2019.163135
Abstract: Abstract We consider the generalized Fokas–Lenells equation which has been become especially popular in recent years for the description soliton solutions in the optical fiber. This equation is studied by us using the traveling wave… read more here.
Keywords: first integrals; lenells equation; general solution; equation ... See more keywords
Characterization of approximate Partial Hamiltonian operators and related approximate first integrals
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DOI: 10.1016/j.ijnonlinmec.2018.06.001
Abstract: Abstract The approximate partial Hamiltonian systems for the characterization of associated approximate operators and first integrals are investigated. It is proved that if an approximate operator is an approximate partial Hamiltonian operator which provides a… read more here.
Keywords: approximate partial; first integrals; partial hamiltonian; operator ... See more keywords
Approximate Hamiltonian symmetries and related first integrals
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DOI: 10.1016/j.ijnonlinmec.2020.103547
Abstract: Abstract We study approximate Hamiltonian symmetries and related first integrals for perturbed Hamiltonian systems. The approximate Hamiltonian symmetry expressed in evolutionary form gives rise to an approximate first integral provided it satisfies certain criteria. We… read more here.
Keywords: approximate hamiltonian; hamiltonian symmetries; first integrals; related first ... See more keywords
On the first integrals of n-th order autonomous systems
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DOI: 10.1016/j.jmaa.2017.11.016
Abstract: The first integrals of n -th order autonomous systems are considered. By getting integrating factors using n−1 n − 1 first integrals of the systems, a necessary condition on the existence of global first integrals… read more here.
Keywords: integrals order; autonomous systems; order autonomous; first integrals ... See more keywords
Meromorphic and formal first integrals for the Lorenz system
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1080/14029251.2018.1440745
Abstract: The Lorenz system , is completely integrable with two functional independent first integrals when σ = 0 and β, r arbitrary. In this paper, we study the integrability of the Lorenz system when σ,β, r… read more here.
Keywords: lorenz system; formal first; first integrals; meromorphic first ... See more keywords
SO(4)-symmetry of mechanical systems with 3 degrees of freedom
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DOI: 10.1080/14029251.2020.1683997
Abstract: We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (4) by means of the… read more here.
Keywords: system; integrals generating; first integrals; mechanical systems ... See more keywords
Rational first integrals of the Liénard equations: The solution to the Poincaré problem for the Liénard equations.
Sign Up to like & getrecommendations! Published in 2021 at "Anais da Academia Brasileira de Ciencias"
DOI: 10.1590/0001-3765202120191139
Abstract: Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class… read more here.
Keywords: poincar; equations solution; first integrals; rational first ... See more keywords
Noether-Type First Integrals Associated with Autonomous Second-Order Lagrangians
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DOI: 10.3390/sym11091088
Abstract: In this paper, the analysis is centered on Noether-type first integrals in Lagrange-Hamilton dynamics based on autonomous second-order Lagrangians. More precisely, by using the classical Noether’s theorem and a non-standard Legendrian duality, the single-time and… read more here.
Keywords: second order; order lagrangians; first integrals; autonomous second ... See more keywords
Integrability and Limit Cycles via First Integrals
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DOI: 10.3390/sym13091736
Abstract: In many problems appearing in applied mathematics in the nonlinear ordinary differential systems, as in physics, chemist, economics, etc., if we have a differential system on a manifold of dimension, two of them having a… read more here.
Keywords: integrability limit; differential systems; limit cycles; first integrals ... See more keywords