A Vector Fokas-Lenells System from the Coupled Nonlinear Schrödinger Equations

Zhang, Meng-Xia; He, ShaoLing; Lv, Shuqiang

doi:10.1080/14029251.2015.996445

Cited by 20 publications

(4 citation statements)

References 25 publications

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“…The system of arising equations for the matrices p and q is formally the same as (52). The number of independent components of each matrix however is now n(n + 1)/2, see for example (84) and (85).…”

Section: CI Symmetric Space Sp(2n)/su(n)mentioning

confidence: 99%

“…The interest to the equations from the "negative" flows is to a big extent related to the variety and complexity of their solutions, [38,40,42,43,6,34,31]. Multi-component generalizations of the FL equation have appeared recently in numerous studies like [14,15,29,31,41,50,51,52,53,44] and this naturally leads to the need of their classification from the viewpoint of the simple Lie algebras, the associated symmetric spaces and their reductions. The other multi-component integrable equations in a non-evolutionary form include for example the massive Thirring-like model, whose integrability was shown by Kuznetsov and Mikhailov [37]; its multicomponent extensions were proposed in [48].…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces

Gerdjikov

Ivanov

2021

Nonlinearity

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Multi-component integrable generalizations of the Fokas-Lenells equation, associated with each irreducible Hermitian symmetric space are formulated. Description of the underlying structures associated to the integrability, such as the Lax representation and the bi-Hamiltonian formulation of the equations is provided. Two reductions are considered as well, one of which leads to a nonlocal integrable model. Examples with Hermitian symmetric spaces of all classical series of types A.III, BD.I, C.I and D.III are presented in details, as well as possibilities for further reductions in a general form.

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Section: CI Symmetric Space Sp(2n)/su(n)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces

Gerdjikov

Ivanov

2021

Nonlinearity

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“…For our study, we write the CFL equations [51] (named for the pioneering works of Fokas [52] and Lenells [53]) as in a normalized form…”

Section: Coupled Fokas-lenells Model and Non-recursive Darboux Transfmentioning

confidence: 99%

General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation

Zhou

Chen

et al. 2019

Proc. R. Soc. A.

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We formulate a non-recursive Darboux transformation technique to obtain the general nth-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and secondorder rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

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“…Many effective methods, such as Riemann-Hilbert method [32], DT [33], non-recursive DT [34], generalized DT [35], etc., have been developed to study on the coupled FL equation. The coupled FL equation is one of the integrable systems as shown in [36] and of course admit other integrable properties including multi-Hamiltonian structure, infinitely many conservation laws, the general soliton solutions [37] and optical soliton [38]. In addition, the baseband MI, rogue wave solutions and state transitions for a deformed FL equation [39] and semi-rational solutions for the coupled derivative NLS equation [40] have been studied by the generalized DT method.…”

Section: Introductionmentioning

confidence: 99%

Modulation instability, conservation laws and localized waves for the generalized coupled Fokas-Lenells equation

Yue,

Chen

2021

Preprint

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This paper focuses on the modulation instability, conservation laws and localized wave solutions of the generalized coupled Fokas-Lenells equation. Based on the theory of linear stability analysis, distribution pattern of modulation instability gain G in the (K, k) frequency plane is depicted, and the constraints for the existence of rogue waves are derived. Subsequently, we construct the infinitely many conservation laws for the generalized coupled Fokas-Lenells equation from the Riccati-type formulas of the Lax pair. In addition, the compact determinant expressions of the N-order localized wave solutions are given via generalized Darboux transformation, including higher-order rogue waves and interaction solutions among rogue waves with bright-dark solitons or breathers. These solutions are parameter controllable: (m i , n i ) and (α, β) control the structure and ridge deflection of solution respectively, while the value of |d| controls the strength of interaction to realize energy exchange. Especially, when d = 0, the interaction solutions degenerate into the corresponding order of rogue waves.

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A Vector Fokas-Lenells System from the Coupled Nonlinear Schrödinger Equations

Cited by 20 publications

References 25 publications

Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces

Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces

General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation

Modulation instability, conservation laws and localized waves for the generalized coupled Fokas-Lenells equation

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