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We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of freedom of
Externí odkaz:
http://arxiv.org/abs/2206.15371
Publikováno v:
Nonlinearity 35 1036 (2022)
We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein-Gordon models. The multi-kinks are constructed using Lin's method from
Externí odkaz:
http://arxiv.org/abs/2106.07063
Publikováno v:
Phys. Rev. Lett. 127, 064101 (2021)
We solve the large deviations of the Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing an approach which combines field theoretical, probabilistic and integrable techniques. We expand the program of the weak noise theor
Externí odkaz:
http://arxiv.org/abs/2103.17215
We present an integrable nonholonomic case of rolling without sliding of a gyroscopic ball over a sphere. This case was introduced and studied in detail by Vasilije Demchenko in his 1923 doctoral dissertation defended at the University of Belgrade, w
Externí odkaz:
http://arxiv.org/abs/2011.03866
Autor:
Alonso, Jaume, Hohloch, Sonja
Publikováno v:
Journal of Nonlinear Science, 31, 51 (2021)
Semitoric systems are a special class of completely integrable systems with two degrees of freedom that have been symplectically classified by Pelayo and Vu Ngoc about a decade ago in terms of five symplectic invariants. If a semitoric system has sev
Externí odkaz:
http://arxiv.org/abs/2006.15369
Autor:
Pallister, Joe
We consider frieze sequences corresponding to sequences of cluster mutations for affine D and E type quivers. We show that the cluster variables satisfy linear recurrences with periodic coefficients, which imply the constant coefficient relations fou
Externí odkaz:
http://arxiv.org/abs/1909.10306
We consider the resonant system of amplitude equations for the conformally invariant cubic wave equation on the three-sphere. Using the local bifurcation theory, we characterize all stationary states that bifurcate from the first two eigenmodes. Than
Externí odkaz:
http://arxiv.org/abs/1807.00426
Autor:
Gaeta, Giuseppe
Publikováno v:
in: Nonlinear Systems and Their Remarkable Mathematical Structures: Volume I (ed. by N. Euler), CRC Press 2018
We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting based on t
Externí odkaz:
http://arxiv.org/abs/1806.06360
Autor:
Tudoran, Răzvan M., Gîrban, Anania
Publikováno v:
Nonlinearity, 30(3), 1058 - 1088 (2017)
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
Comment: 35 pages
Comment: 35 pages
Externí odkaz:
http://arxiv.org/abs/1602.03196
Autor:
Calogero, Francesco
Publikováno v:
SIGMA 7 (2011), 082, 35 pages
The original continuous-time "goldfish" dynamical system is characterized by two neat formulas, the first of which provides the $N$ Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding in
Externí odkaz:
http://arxiv.org/abs/1108.4492