Branched-dispersion generalizations of Lotka–Volterra and Ablowitz–Ladik nonlinear integrable systems revisited from the intersite coupling standpoint

Vakhnenko, Oleksiy O.; Verchenko, Andriy P.

doi:10.1016/j.physleta.2022.128460

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…For any 𝑀 and 𝑁 = 1, on the components, system (2) becomes coupled semidiscrete Lotka-Volterra system [23,24] and has the following expression:…”

Section: The Coupled Semidiscrete Lotka-volterra Systemmentioning

confidence: 99%

Coupled discrete solitonic equations of additive Bogoyavlensky and the periodic reduction

Babalic

2023

Proceedings of 11th International Conference of the Balkan Physical Union — PoS(BPU11)

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Using the Hirota bilinear formalism we build the Hirota bilinear form and construct the multisoliton solutions for the coupled semidiscrete additive Bogoyavlensky system with branched dispersion, proving its complete integrability. The same result can be reached also applying the periodic reduction technique. Starting from a general completely integrable "diagonal" equation in two dimensions and performing periodic reduction, one can obtain coupled completely integrable equations. The idea is to consider that the independent discrete variable of the analysed equation is in fact diagonal in a two-dimensional lattice. Imposing periodic reduction on one such coordinate in the 2D-lattice, one can obtain coupled integrable systems with branched disperssion. We will exemplify the technique on the semidiscrete additive Bogoyavlensky equation (aB), which is an integrable semidiscrete generalized Volterra type equation.

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“…For any 𝑀 and 𝑁 = 1, on the components, system (2) becomes coupled semidiscrete Lotka-Volterra system [23,24] and has the following expression:…”

Section: The Coupled Semidiscrete Lotka-volterra Systemmentioning

confidence: 99%

Coupled discrete solitonic equations of additive Bogoyavlensky and the periodic reduction

Babalic

2023

Proceedings of 11th International Conference of the Balkan Physical Union — PoS(BPU11)

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Discrete periodic solitons and dynamical analysis for an integrable coupled inhomogeneous lattice

Yuan,

Liu,

Yang

et al. 2024

Chaos, Solitons & Fractals

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Rogue wave patterns to the artificial synchronization of three uncoupled Ablowitz−Ladik systems in the framework of Babalic−Cârstea auxiliary Lax representation

Lin

Wen

2022

Eur. Phys. J. Plus

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Branched-dispersion generalizations of Lotka–Volterra and Ablowitz–Ladik nonlinear integrable systems revisited from the intersite coupling standpoint

Cited by 4 publications

References 30 publications

Coupled discrete solitonic equations of additive Bogoyavlensky and the periodic reduction

Coupled discrete solitonic equations of additive Bogoyavlensky and the periodic reduction

Discrete periodic solitons and dynamical analysis for an integrable coupled inhomogeneous lattice

Rogue wave patterns to the artificial synchronization of three uncoupled Ablowitz−Ladik systems in the framework of Babalic−Cârstea auxiliary Lax representation

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