Integrable discretizations of derivative nonlinear Schr dinger equations

Tsuchida, Takayuki

doi:10.1088/0305-4470/35/36/310

Cited by 81 publications

(123 citation statements)

References 64 publications

(110 reference statements)

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“…This correspondence is not surprising as their respective "ancestor" systems (3.1) and (3.16) are connected through the same type of transformation [23].…”

Section: System Of Coupled Derivative Mkdv Equations (222)mentioning

confidence: 82%

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New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

Tsuchida

2010

Journal of Mathematical Physics

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We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.

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“…This correspondence is not surprising as their respective "ancestor" systems (3.1) and (3.16) are connected through the same type of transformation [23].…”

Section: System Of Coupled Derivative Mkdv Equations (222)mentioning

confidence: 82%

“…It can be recalled that an integrable semi-discretization of the third-order matrix KaupNewell system (2.19) is given by [23] q n,t + ∆ n (I 1 − q n r n ) −1 q n + (…”

Section: System Of Coupled Derivative Mkdv Equations (222)mentioning

confidence: 99%

New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

Tsuchida

2010

Journal of Mathematical Physics

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“…The functions c 11 (n) and c 33 (n) referred to as the sampling ones remain arbitrary for the time being. The similar situation with the unfixed sampling is typical of other integrable models [40,47] and can be resolved relying upon the local conservation laws [48,49] dictated by the matrix structure of proposed spectral operator (2.2).…”

Section: Auxiliary Spectral and Evolution Operatorsmentioning

confidence: 86%

Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

Vakhnenko

2021

JNMP

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The new type of third-order spectral operator suitable to generate new multifield semidiscrete nonlinear systems with two coupling parameters in the framework of zero-curvature equation is proposed. The evolution operator corresponding to the first integrable system in an infinite hierarchy is explicitly recovered and the general form of first integrable system is isolated. The generalized procedure for the direct recursive development of infinite hierarchy of local conservation laws is presented and several lowest local conservation laws and local conserved densities are found. The reduction to the real field amplitudes in general system with unfixed sampling functions is made and the symmetric parametrization of field amplitudes allowing to exclude the redundant field function and to resolve the problem of sampling fixation for the particular realization of reduced integrable system is considered. This parametrization gives rise to the four field nonlinear model which in certain intervals of adjustable coupling parameter could serve as a semidiscrete analogy to the beam-plasma interaction system.

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“…and require selecting zero constant for the inverse operation of the difference operator ( − 1) in computing ( ) ( ≥ 1), then the recursion relation (14) Proof. From (9), we know that…”

Section: An Integrable Different-difference Family and Its Hamiltoniamentioning

confidence: 99%

A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation

Xü

2018

Discrete Dynamics in Nature and Society

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An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established. Liouville integrability for the obtained family of discrete Hamiltonian systems is proved. Based on the gauge transformation between the Lax pair, a Darboux-Bäcklund transformation of the first nonlinear different-difference equation in obtained family is deduced. Using this Darboux-Bäcklund transformation, an exact solution is presented.

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Integrable discretizations of derivative nonlinear Schr dinger equations

Cited by 81 publications

References 64 publications

New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation

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