(2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion

Salih Yaman; Devrim Yazıcı

(2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion

Abstract

In this work, we investigate a symmetry reduction of the recently discovered (3 + 1)-dimensional equation of the Monge-Ampère type. This equation forms a bi-Hamiltonian system using Magri’s theorem when expressed in the two-component form. We select a particular linear combination of the Lie point symmetries belonging to this system to conduct symmetry reduction, resulting in a new (2 + 1)-dimensional system in two-component form. Lagrangian and first Hamiltonian densities are then calculated. We employ Dirac’s theory of constraints to obtain symplectic and first Hamiltonian operators. Subsequently, we transform the symmetry condition of the reduced system into a skew-factorized form to determine the recursion operator. Applying the recursion operator to the first Hamiltonian operator yields the second Hamiltonian operator. We demonstrate that the reduced system is a bi-Hamiltonian integrable system in the sense of Magri. Lie point symmetries of the reduced system are identified. Finally, we calculate integrals of motion using the inverse Noether theorem and prove that they have the total divergence form.

Keywords

References

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Details

Primary Language

English

Subjects

Clinical Chemistry

Journal Section

Research Article

Authors

Salih Yaman
0000-0002-6956-0319
Türkiye

Devrim Yazıcı ^*
0000-0002-1227-3773
Türkiye

Publication Date

December 9, 2024

Submission Date

July 19, 2023

Acceptance Date

December 29, 2023

Published in Issue

Year 2024 Volume: 42 Number: 6

IZ

https://izlik.org/JA58YY97CU

Cite

RIS / Bibtex

APA

Yaman, S., & Yazıcı, D. (2024). (2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion. Sigma Journal of Engineering and Natural Sciences, 42(6), 1838-1846. https://izlik.org/JA58YY97CU

AMA

1.Yaman S, Yazıcı D. (2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion. SIGMA. 2024;42(6):1838-1846. https://izlik.org/JA58YY97CU

Chicago

Yaman, Salih, and Devrim Yazıcı. 2024. “(2+1)-Dimensional New Bi-Hamiltonian Integrable System: Symmetries, Noether’s Theorem and Integrals of Motion”. Sigma Journal of Engineering and Natural Sciences 42 (6): 1838-46. https://izlik.org/JA58YY97CU.

EndNote

Yaman S, Yazıcı D (December 1, 2024) (2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion. Sigma Journal of Engineering and Natural Sciences 42 6 1838–1846.

IEEE

[1]S. Yaman and D. Yazıcı, “(2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion”, SIGMA, vol. 42, no. 6, pp. 1838–1846, Dec. 2024, [Online]. Available: https://izlik.org/JA58YY97CU

ISNAD

Yaman, Salih - Yazıcı, Devrim. “(2+1)-Dimensional New Bi-Hamiltonian Integrable System: Symmetries, Noether’s Theorem and Integrals of Motion”. Sigma Journal of Engineering and Natural Sciences 42/6 (December 1, 2024): 1838-1846. https://izlik.org/JA58YY97CU.

JAMA

1.Yaman S, Yazıcı D. (2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion. SIGMA. 2024;42:1838–1846.

MLA

Yaman, Salih, and Devrim Yazıcı. “(2+1)-Dimensional New Bi-Hamiltonian Integrable System: Symmetries, Noether’s Theorem and Integrals of Motion”. Sigma Journal of Engineering and Natural Sciences, vol. 42, no. 6, Dec. 2024, pp. 1838-46, https://izlik.org/JA58YY97CU.

Vancouver

1.Salih Yaman, Devrim Yazıcı. (2+1)-dimensional new bi-hamiltonian integrable system: Symmetries, Noether’s theorem and integrals of motion. SIGMA [Internet]. 2024 Dec. 1;42(6):1838-46. Available from: https://izlik.org/JA58YY97CU