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The classical limit of non-integrable quantum systems [PDF]
, 2005 The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system.
Castagnino, Mario, Lombardi, Olimpia
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Overview of the Kadomtsev–Petviashvili-hierarchy reduction method for solitons
Partial Differential Equations in Applied Mathematics, 2022 The Kadomtsev–Petviashvili (KP) hierarchy reduction method is a prominent direct method for deriving explicit solutions to integrable equations. This method is based on Hirota’s bilinear formulation of integrable systems, as well as the observation that ...
Bo Yang, Jianke Yang
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NORMALIZATION OF CLASSICAL HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM
Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2020 The family of the Hamiltonian systems with two degrees of freedom was investigated. The calculations of the Poincaré sections show that with arbitrary values of the parameters of the Hamilton function, the system is non-integrable and dynamic chaos is ...
I.N. Belyaeva +4 more
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Journal of High Energy Physics, 2023 Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm.
S. Y. Lou, Xia-zhi Hao, Man Jia
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Hypercomplex integrable systems [PDF]
Nonlinearity, 1999 In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds.
Grant, James D. E., Strachan, I. A. B.
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Discrete Values of the Coefficient of Damping under Conditions of Explicit Acoustic Nonlinearity
Nonlinear Analysis, 2006 Qualitative analysis of hypersound generation is described by the inhomogeneous Burgers equation in the case of the non-harmonic and arbitrary light field. A qualitative possibility of the appearance of discrete values of the coefficient of extinction of
P. Miškinis
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Partial Differential Equations in Applied Mathematics, 2022 The complex coupled integrable dispersionless (CID)system is an important system. It has been shown that complex CID equation is gauge equivalent to the Pohlmeyer–Lund–Regge model (a complex sine-Gordon equation) and can also be transformed to the ...
Caiqin Song, Chen-Chen Fu, Zuo-Nong Zhu
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Dispersionless Limit of Integrable Models [PDF]
, 2002 Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type.
Brunelli, J. C.
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On the complete integrability of an equation having solitons but not known to have a Lax pair
International Journal of Mathematics and Mathematical Sciences, 1986 It is usually assumed that a system having N-soliton solutions is completely integrable. Here we have analyzed a set of equations occuring in case of capillary gravity waves.
A. Roychowdhury, G. Mahato
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A generalized isospectral–nonisospectral heat equation hierarchy and its expanding integrable model
Advances in Difference Equations, 2020 A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati ...
Huanhuan Lu, Yufeng Zhang, Jianqin Mei
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