Domain walls in a non-linear S 2 $$ {\mathbb{S}}^2 $$ -sigma model with homogeneous quartic polynomial potential [PDF]
Journal of High Energy Physics, 2018 In this paper the domain wall solutions of a Ginzburg-Landau non-linear S 2 $$ {\mathbb{S}}^2 $$ -sigma hybrid model are exactly calculated. There exist two types of basic domain walls and two families of composite domain walls. The domain wall solutions
A. Alonso-Izquierdo +2 more
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Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree −2 [PDF]
Physics Letters A, 2011 Agraïments: The third author is partially supported by FCT through CAMGDS, Lisbon. We characterize the analytic integrability of Hamiltonian systems with Hamiltonian H = 1/ 2 2∑ i=1 p 2 i + V (q1, q2), having homogeneous potential V (q1, q2) of degree −2.
Llibre, Jaume +2 more
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Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4 [PDF]
Journal of Mathematical Physics, 2011 In the analytic case we prove the conjecture of Maciejewski and Przybylska [J. Math. Phys. 46(6), 062901 (2005)] regarding Hamiltonian systems with a homogeneous polynomial potential of degree 4. The proof of the conjecture completes the characterization of all the analytic integrable Hamiltonian system with a homogeneous polynomial potential of degree
Llibre, Jaume +2 more
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A note on the integrability of exceptional potentials via polynomial bi-homogeneous potentials
Bulletin of Computational Applied Mathematics, 2021 This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree $k$ of type $V_{k,l}=α(q_2-i q_1)^l (q_2+iq_1)^{k-l}$ with $α\in\mathbb{C}$ and $l=0,1,\dots, k$, called exceptional potentials.
Primitivo B. Acosta-Humánez +2 more
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Monoparametric Families of Orbits Produced by Planar Potentials
Axioms, 2023 We study the motion of a test particle on the xy−plane. The particle trajectories are given by a one-parameter family of orbits f(x,y) = c, where c = const.
Thomas Kotoulas
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020 The possibility of constructing a full-parametric analytical solution of the stress-strain state problem for the body caused by the influence of volumetric forces is studied.
Viktor Borisovich Pen'kov +2 more
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Inflation without a trace of lambda
European Physical Journal C: Particles and Fields, 2020 We generalise Einstein’s formulation of the traceless Einstein equations to f(R) gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally ...
John D. Barrow, Spiros Cotsakis
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A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta [PDF]
Journal of Physics A: Mathematical and General, 2001 22 pages, no figures, to appear in J. Phys.
Nakagawa, Katsuya, Yoshida, Haruo
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Finiteness of integrable n-dimensional homogeneous polynomial potentials [PDF]
Physics Letters A, 2007 We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable. We also explain how to find explicit forms of these integrable potentials for small $k$.
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On the integrability of the Hamiltonian systems with homogeneous polynomial potentials [PDF]
Applied Mathematics and Nonlinear Sciences, 2018 Abstract We summarize the known results on the integrability of the complex Hamiltonian systems with two degrees of freedom defined by the Hamiltonian functions of the form
Llibre, Jaume, Zhang, Xiang
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