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 $V_{k,l}=\alpha (q_2-i q_1)^l (q_2+iq_1)^{k-l}$ with $\alpha$ in C and l=0 ...
Primitivo B. Acosta-Humánez +2 more
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Long-time behavior of stochastic reaction–diffusion equation with multiplicative noise
Advances in Difference Equations, 2020 In this paper, we study the dynamical behavior of the solution for the stochastic reaction–diffusion equation with the nonlinearity satisfying the polynomial growth of arbitrary order p ≥ 2 $p\geq2$ and any space dimension N.
Jing Wang, Qiaozhen Ma, Tingting Liu
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Classical planar algebraic curves realizable by quadratic polynomial differential systems [PDF]
, 2017 In this paper we show planar quadratic polynomial differentialsystems exhibiting as solutions some famous planar invariant algebraic curves. Also we put particular attention to the Darboux integrability of these differential systems.The author is ...
García, I. A. (Isaac A.), Llibre, Jaume
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From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition
, 2000 The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is
Arnold V I +17 more
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, 2010 Based on the gradient-holonomic algorithm we analyze the integrability property of the generalized hydrodynamical Riemann type equation $%D_{t}^{N}u=0$ for arbitrary $N\in \mathbb{Z}_{+}.$ The infinite hierarchies of polynomial and non-polynomial ...
Popowicz, Ziemowit +1 more
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Integrability via geometry: dispersionless differential equations in three and four dimensions [PDF]
, 2019 We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein-Weyl ...
Calderbank, David M. J. +1 more
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Adiabatic gauge potential and integrability breaking with free fermions
SciPost PhysicsWe revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos.
Balázs Pozsgay, Rustem Sharipov, Anastasiia Tiutiakina, István Vona
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Geometry and integrability of quadratic systems with invariant hyperbolas
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Let QSH be the family of non-degenerate planar quadratic differential systems possessing an invariant hyperbola. We study this class from the viewpoint of integrability.
Regilene Oliveira +2 more
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Integrability of planar polynomial differential systems through linear differential equations [PDF]
, 2005 In this work, we consider rational ordinary differential equations dy/dx = Q(x,y)/P(x,y), with Q(x,y) and P(x,y) coprime polynomials with real coefficients.
Giacomini, Héctor +2 more
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On some orthogonal polynomial integrals [PDF]
Mathematics of Computation, 1980 The modified moments of the weight functions w ( x ) = x ρ ( 1 − x ) a ln ( 1 / x ) w(x) = {x^\rho }{(1 - x ...
openaire +2 more sources