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The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this arti
Externí odkaz:
http://arxiv.org/abs/2405.07912
Publikováno v:
Physica D: Nonlinear Phenomena, Volume 453, 2023, 133826
This paper proposes a new uncertainty measure, appropriate for quantifying the performance of transport models in assessing the origin or source of a given observation. It is found that in a neighbourhood of the observation the proposed uncertainty m
Externí odkaz:
http://arxiv.org/abs/2401.14760
Autor:
Agaoglou, Makrina, Feckan, Michal, Pospisil, Michal, Rothos, Vassilis M., Vakakis, Alexander F.
Publikováno v:
Axioms 2018, 7(4), 69
In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced system.
Externí odkaz:
http://arxiv.org/abs/2401.14227
Publikováno v:
Journal of Differential Equations, Volume 260, Issue 2, 2016, Pages 1717-1746
We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results of periodic
Externí odkaz:
http://arxiv.org/abs/2401.14108
Publikováno v:
International Journal of Bifurcation and Chaos, Vol. 24, No. 11, 1450147 (2014)
In this work, we study a model of a one-dimensional magnetic metamaterial formed by a discrete array of nonlinear resonators. We focus on periodic and localized traveling waves of the model, in the presence of loss and an external drive. Employing a
Externí odkaz:
http://arxiv.org/abs/2401.13846
Autor:
Han, Yanwei, Zhang, Zijian
The nonlinear energy harvesting systems of the forced vibration with an electron-mechanical coupling are widely used to capture ambient vibration energy and convert mechanical energy into electrical energy. However, the nonlinear response mechanism o
Externí odkaz:
http://arxiv.org/abs/2312.17282
Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a Liouvillian first integral (belonging to a vast class of Liouvillian f
Externí odkaz:
http://arxiv.org/abs/2310.04850
We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid theoretical basis through a relation between the 1ODE we a
Externí odkaz:
http://arxiv.org/abs/2308.12391
Publikováno v:
Chaos, Solitons & Fractals Volume 177, December 2023, 114232
Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries) algorithmically.
Externí odkaz:
http://arxiv.org/abs/2306.13221
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results using the G
Externí odkaz:
http://arxiv.org/abs/2306.09978