Classical Energy Spectrum of the Hirota Nonlinear Oscillator

Laptev, Denis V.

doi:10.7566/jpsj.82.044005

Cited by 6 publications

(11 citation statements)

References 20 publications

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“…One more example of the systems with 'friction' is the nonlinear Hirota oscillator playing an extremely important role in the study of nonlinear evolution equations and dynamical systems [24,25]. Its equation of motion and the Lagrange function areφ + (1 +φ 2 ) tan φ = 0,…”

Section: Discussionmentioning

confidence: 99%

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

2018

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We give an example of a simple mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. This system is a linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed, the simplest system with broken T -invariance. The paradoxical character of the presented results is that the same Hamiltonian system, the generalized harmonic oscillator in our case, is canonically equivalent to two different systems: the usual plane mathematical pendulum and the damped harmonic oscillator. This once again supports the important mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems, which stems from the Sonin theorem that any Newtonian second order differential equation with a friction of general nature may be presented in the form of the Lagrange equation.

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Section: Discussionmentioning

confidence: 99%

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

2018

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“…Since the function dn(θ,μ) ≠ 0, ∀θ zero-fixed boundary conditions (13) are not satisfied for the solution (14).…”

Section: The Superlattices Of the Discrete Breathers And Shock Wavesmentioning

confidence: 99%

“…In this paper the properties of single DBs and the superlattices of DBs in the exactly intagrable model of the anharmonic atomic chain -Hirota lattice -is considered [9][10][11][12][13][14][15]. The exactly integrable models of the lattice systems are important because for these models it is often possible to obtain the analytic expressions for the lattice excitations and for their main physical characteristics such as energy, momentum, etc.…”

Section: The 1d Hirota Lattice Modelmentioning

confidence: 99%

“…Expression (28) is the energy (6) of the standing discrete breather superlattice of type I (14) in the chain with N nodes for the moment of time t = 0. …”

Section: The Superlattices Of the Discrete Breathers And Shock Wavesmentioning

confidence: 99%

“…The evolution of the lattice was modelled using the initial conditions corresponding to the breather superlattice of type I (SLI) (14) with linear sinusoidal perturbation.…”

Section: The Superlattices Of the Discrete Breathers And Shock Wavesmentioning

confidence: 99%

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The superlattices of discrete breathers in the model of the 1D crystal

Laptev¹

2016

LoM

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The dynamics of the discrete breather superlattices in the model of the 1D anharmonic Hirota lattice is considered. The analogues of the discrete breather for the finite-size system with periodic boundary conditions are presented. For the analogue of the discrete breather for the finite-size system the stability and the effect of dissipation on the dynamics are discussed. Using the exact solutions of the Hirota lattice equation in the form of discrete breather superlattices the asymptotic interaction energy between two breathers is investigated. It is shown that for the considered parameters of the solutions discrete breathers in the superlattice of type I repel, while in the superlattice of type II attract each other.

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Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

Ghose‐Choudhury

Guha

2022

Qual. Theory Dyn. Syst.

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Classical Energy Spectrum of the Hirota Nonlinear Oscillator

Cited by 6 publications

References 20 publications

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

The superlattices of discrete breathers in the model of the 1D crystal

Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

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