Integrable fourth-order difference equations

Maheswari, C Uma; Sahadevan, R.

doi:10.1088/1751-8113/43/23/235203

Cited by 4 publications

(1 citation statement)

References 28 publications

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“…We have verified that equation (3.10) is a measure preserving one with measure 1 [−Q 1 (n)+Q 2 (n)] [32].…”

Section: R Sahadevan and G Nagavigneshwarimentioning

confidence: 70%

New Integrable and Linearizable Nonlinear Difference Equations

Sahadevan¹,

Nagavigneshwari²

2021

JNMP

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A systematic investigation to derive nonlinear lattice equations governed by partial difference equations (PΔΔE) admitting specific Lax representation is presented. Further it is shown that for a specific value of the parameter the derived nonlinear PΔΔE's can be transformed into a linear PΔΔE's under a global transformation. Also it is demonstrated how to derive higher order ordinary difference equations (OΔE) or mappings in general and linearizable ones in particular from the obtained nonlinear PΔΔE's through periodic reduction. The question of measure preserving property of the obtained OΔE's and the construction of more than one integrals (or invariants) of them is examined wherever possible.

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“…We have verified that equation (3.10) is a measure preserving one with measure 1 [−Q 1 (n)+Q 2 (n)] [32].…”

Section: R Sahadevan and G Nagavigneshwarimentioning

confidence: 70%

New Integrable and Linearizable Nonlinear Difference Equations

Sahadevan¹,

Nagavigneshwari²

2021

JNMP

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Lax integrable nonlinear partial difference equations

Sahadevan

Nagavigneshwari

2015

Communications in Nonlinear Science and Numerical Simulation

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Painlevé analysis, Prelle–Singer approach, symmetries and integrability of damped Hénon–Heiles system

Uma Maheswari,

Muthuchamy,

Chandrasekar

et al. 2024

Journal of Mathematical Physics

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We consider a modified damped version of Hénon–Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon–Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle–Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon–Heiles system. We infer that the modified Hénon–Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.

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Integrable fourth-order difference equations

Cited by 4 publications

References 28 publications

New Integrable and Linearizable Nonlinear Difference Equations

New Integrable and Linearizable Nonlinear Difference Equations

Lax integrable nonlinear partial difference equations

Painlevé analysis, Prelle–Singer approach, symmetries and integrability of damped Hénon–Heiles system

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