On the symmetries of a nonlinear non-polynomial oscillator

Mohanasubha, R.; Senthilvelan, M.

doi:10.1016/j.cnsns.2016.06.013

Cited by 6 publications

(2 citation statements)

References 38 publications

(69 reference statements)

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“…In this section, the bi-Hamiltonian structures of lattice hierarchies on the regular discrete obtained in the preceding section by means of the R-matrix method [30,31] are investigated. One of the advantages of the classical R-matrix approach is to construct bi-Hamiltonian structures.…”

Section: R-matrix Theory For Bi-hamiltonian Structures On the Regular...mentioning

confidence: 99%

N-Dimensional Lattice Integrable Systems and Their bi-Hamiltonian Structure on the Time Scale Using the R-Matrix Approach

Fang,

Sang,

Yuen

et al. 2024

Axioms

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A time scale is a special measure chain that can unify continuous and discrete spaces, enabling the construction of integrable equations. In this paper, with the Lax operator generated by the displacement operator, N-dimensional lattice integrable systems on the time scale are given by the R-matrix approach. The recursion operators of the lattice systems are derived on the time scale. Finally, two integrable hierarchies of the discrete chain with a bi-Hamiltonian structure are obtained. In particular, we give the structure of two-field and four-field systems.

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Section: R-matrix Theory For Bi-hamiltonian Structures On the Regular...mentioning

confidence: 99%

N-Dimensional Lattice Integrable Systems and Their bi-Hamiltonian Structure on the Time Scale Using the R-Matrix Approach

Fang,

Sang,

Yuen

et al. 2024

Axioms

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“…• Absence of cubic and quintic nonlinear terms (i.e., 0 1 ≠ α , 0 2 ≠ α , 3 0 α = and 0 4 = α ): the equation can be used to model a physical particle on a rotating parabola [3,21] and a nonpolynomial oscillator [22].…”

Section: Motivationmentioning

confidence: 99%

Analysis of Large-Amplitude Oscillations in Triple-Well Non-Natural Systems

Lai

Yang

Gao

2019

Journal of Computational and Nonlinear Dynamics

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In this paper, the large-amplitude oscillation of a triple-well non-natural system, covering both qualitative and quantitative analysis, is investigated. The nonlinear system is governed by a quadratic velocity term and an odd-parity restoring force having cubic and quintic nonlinearities. Many mathematical models in mechanical and structural engineering applications can give rise to this nonlinear problem. In terms of qualitative analysis, the equilibrium points and its trajectories due to the change of the governing parameters are studied. It is interesting that there exist heteroclinic and homoclinic orbits under different equilibrium states. By adjusting the parameter values, the dynamic behavior of this conservative system is shifted accordingly. As exact solutions for this problem expressed in terms of an integral form must be solved numerically, an analytical approximation method can be used to construct accurate solutions to the oscillation around the stable equilibrium points of this system. This method is based on the harmonic balance method incorporated with Newton's method, in which a series of linear algebraic equations can be derived to replace coupled and complicated nonlinear algebraic equations. According to this harmonic balance-based approach, only the use of Fourier series expansions of known functions is required. Accurate analytical approximate solutions can be derived using lower order harmonic balance procedures. The proposed analytical method can offer good agreement with the corresponding numerical results for the whole range of oscillation amplitudes.

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