Multi‐component integrable couplings for the Ablowitz–Kaup–Newell–Segur and Volterra hierarchies

Shen, Shoufeng; Li, Chunxia; Jin, Yongyang; Yu, Shuimeng

doi:10.1002/mma.3372

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…When ε = 0, it reduces the case of vector AKNS integrable couplings [22,23]. Based on thus spectral matrix, we can work out the complete system of the vector AKNS integrable couplings by standard procedure.…”

Section: Completion Of the Vector Akns Integrable Couplingsmentioning

confidence: 99%

Completion of the integrable coupling systems

Yao,

Li,

Shen

2017

Preprint

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In this paper, we proposed an procedure to construct the completion of the integrable system by adding a perturbation to the generalized matrix problem, which can be used to continuous integrable couplings, discrete integrable couplings and super integrable couplings. As example, we construct the completion of the Kaup-Newell (KN) integrable coupling, the Wadati-Konno-Ichikawa (WKI) integrable couplingsis, vector Ablowitz-Kaup-Newell-Segur (vAKNS) integrable couplings, the Volterra integrable couplings, Dirac type integrable couplings and NLS-mKdV type integrable couplings.

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Section: Completion Of the Vector Akns Integrable Couplingsmentioning

confidence: 99%

Completion of the integrable coupling systems

Yao,

Li,

Shen

2017

Preprint

Self Cite

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show abstract

“…Recently, Shen et al considered a generalized spatial spectral problem of AKNS integrable coupling as follows:

ϕ_{x} = U ϕ, U = ((), \begin{matrix} array λ + ω & array p & array 0 & array r \\ array q & array - λ - ω & array s & array 0 \\ array 0 & array 0 & array λ + ω & array p \\ array 0 & array 0 & array q & array - λ - ω \end{matrix}), ϕ = ((), \begin{matrix} array ϕ_{1} \\ array ϕ_{2} \\ array ϕ_{3} \\ array ϕ_{4} \end{matrix}), u = ((), \begin{matrix} array p \\ array q \\ array r \\ array s \end{matrix}),

where ω = ϵ ( p s + q r ); λ is the spectral parameter; and p , q , r , and s are commuting variables. Obviously, when ϵ =0, this generalized spatial spectral problem is reduced to a new case of AKNS integrable couplings, whose bi‐Hamiltonian structures were constructed by using the component‐trace identity in . Inspired by those spatial spectral problems, in this paper, we would like to construct nonlinear super integrable couplings of a generalized super AKNS hirearchy.…”

Section: Introductionmentioning

confidence: 99%

“…where ω = ǫ(ps + qr) and λ is the spectral parameter, p, q, r and s are commuting variables. Obviously, when ǫ = 0, this generalized spatial spectral problem (1.2) is reduced to a new case of AKNS integrable couplings [47]. Whose bi-Hamiltonian structures were constructed by using the component-trace identity in [46].…”

Section: Introductionmentioning

confidence: 99%