Infinite-dimensional 3-algebra and integrable system

Chen, Min-Ru; Wang, Shikun; Wu, Ke; Wang, Zhao

doi:10.1007/jhep12(2012)030

Cited by 20 publications

(15 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the generators T n (36), we note that they are the associative operators with the product (37). According to the definition of the n-bracket (21), we get the following result.…”

Section: (Co)sine N-algebramentioning

confidence: 97%

“…Let us turn to the case of 3-algebra. Substituting the generators (36) into the operator Nambu 3-bracket (18) and using (37) and (38), by direct calculation, we may derive the following 3-algebra:…”

Section: Q-deformed V-w N-algebramentioning

confidence: 99%

“…Moreover the relation between the infinite-dimensional 3-algebras and the integrable systems has also been studied. [37,38].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On q-deformed infinite-dimensional n-algebra

Ding

Jia

et al. 2016

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

The q-deformation of the infinite-dimensional n-algebra is investigated. Based on the structure of the q-deformed Virasoro-Witt algebra, we derive a nontrivial q-deformed Virasoro-Witt n-algebra which is nothing but a sh-n-Lie algebra. Furthermore in terms of the pseuddifferential operators on the quantum plane, we construct the (co)sine n-algebra and the q-deformed SDif f (T 2 ) n-algebra. We prove that they are the sh-n-Lie algebras for the case of even n. An explicit physical realization of the (co)sine n-algebra is given.

show abstract

“…For the generators T n (36), we note that they are the associative operators with the product (37). According to the definition of the n-bracket (21), we get the following result.…”

Section: (Co)sine N-algebramentioning

confidence: 97%

Section: Q-deformed V-w N-algebramentioning

confidence: 99%

See 1 more Smart Citation

On q-deformed infinite-dimensional n-algebra

Ding

Jia

et al. 2016

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the W 1+∞ constraints (15), it is noted that the constraint operators (14) contain the operators increasing and preserving the grading. Let us now introduce the following operators in terms of the operators decreasing and preserving the grading:…”

Section: Let Us Introduce the Operatorsmentioning

confidence: 99%

Exact correlators in the Gaussian Hermitian matrix model

Kang

Yan

et al. 2019

Physics Letters B

Self Cite

View full text Add to dashboard Cite

show abstract

“…Chen er al. [42] investigated the classical Heisenberg and w ∞ 3-algebras and established the relation between the dispersionless KdV hierarchy and these two infinite-dimensional 3-algebras. They found that the dispersionless KdV system is not only a bi-Hamiltonian system, but also a bi-Nambu-Hamiltonian system.…”

Section: Introductionmentioning

confidence: 99%

OnW1+∞3-algebra and integrable system

Chen

Wang

et al. 2015

Nuclear Physics B

Self Cite

View full text Add to dashboard Cite

We construct the W 1+∞ 3-algebra and investigate the relation between this infinitedimensional 3-algebra and the integrable systems. Since the W 1+∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W 1+∞ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the W 1+∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the W 1+∞ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of W 1+∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrödinger equation and give an application in optical soliton.

show abstract

Infinite-dimensional 3-algebra and integrable system

Cited by 20 publications

References 54 publications

On q-deformed infinite-dimensional n-algebra

On q-deformed infinite-dimensional n-algebra

Exact correlators in the Gaussian Hermitian matrix model

OnW1+∞3-algebra and integrable system

Contact Info

Product

Resources

About