Bi-integrable couplings of a Kaup–Newell type soliton hierarchy and their bi-Hamiltonian structures

Yu, Shuimeng; Yao, Yuqin; Shen, Shoufeng; Ma, Wen‐Xiu

doi:10.1016/j.cnsns.2014.12.008

Cited by 5 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because the associated matrix Lie algebras are nonsemisimple, we should use the variational identity (11) to furnish the Hamiltonian structures of the integrable couplings system (58) (or (59)). Before doing this, we should find out the nondegenerate, symmetric, and adinvariant bilinear form corresponding to the nonsemisimple matrix loop algebras first [22]. By defining a mapping from to 9 as :…”

Section: Bi-hamiltonian Structures and Liouville Integrability Of Thementioning

confidence: 99%

“…we have the following results according to [22,28,30]. The mapping (61) is a Lie algebra isomorphism from to 9 and the Lie bracket [⋅, ⋅] can be calculated as…”

Section: Bi-hamiltonian Structures and Liouville Integrability Of Thementioning

confidence: 99%

“…In order to solve this problem, Ma proposes the variational identity [19] while Guo and Zhang propose the quadratic-form identity [20]. By using them, the Hamiltonian structures of many integrable couplings systems have been furnished [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

Zhang

Yao

2016

Advances in Mathematical Physics

Self Cite

View full text Add to dashboard Cite

A new type of two-component Casimir-Qiao-Liu type hierarchy (2-CQLTH) is produced from a new spectral problem and their bi-Hamiltonian structures are constructed. Particularly, a new completely integrable two-component Casimir-Qiao-Liu type equation (2-CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of3×3block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.

show abstract

Section: Bi-hamiltonian Structures and Liouville Integrability Of Thementioning

confidence: 99%

“…we have the following results according to [22,28,30]. The mapping (61) is a Lie algebra isomorphism from to 9 and the Lie bracket [⋅, ⋅] can be calculated as…”

Section: Bi-hamiltonian Structures and Liouville Integrability Of Thementioning

confidence: 99%

See 1 more Smart Citation

The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

Zhang

Yao

2016

Advances in Mathematical Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, it has been applied to the theory of nonlinear systems [23][24][25][26]. Its structure matrix and damping matrix provide more energy information as the theory of the generalized Hamiltonian system develops.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

Chen

Zhang

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, an universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional  and the time-lag  on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

show abstract

Bi-Integrable Couplings Associated with so $$(3,{\mathbb R})$$ ( 3 , R )

McAnally

2017

Bull. Malays. Math. Sci. Soc.

View full text Add to dashboard Cite

Bi-integrable couplings of a Kaup–Newell type soliton hierarchy and their bi-Hamiltonian structures

Cited by 5 publications

References 41 publications

The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag

Bi-Integrable Couplings Associated with so $$(3,{\mathbb R})$$ ( 3 , R )

Contact Info

Product

Resources

About