Strong and weak interactions of rational vector rogue waves and solitons to any<i>n</i>-component nonlinear Schrödinger system with higher-order effects

Weng, Weifang; Zhang, Guoqiang; Yan, Zhenya

doi:10.1098/rspa.2021.0670

Cited by 6 publications

(3 citation statements)

References 78 publications

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“…The spin soliton solutions in [34] exist in the surface that admits F 2 = F 4 . Last, but not least, it is worth mentioning that the integrable cases have been widely studied and various exact soliton solutions have been obtained, based on methods such as the inverse-scattering method [48], the Hirota bilinear method [49] and the Darboux transformation method [50,51]. A series of multi-soliton solutions can be provided by multiple iterations, but there were strong constraints on the coefficients.…”

Section: Constraint Conditionsmentioning

confidence: 99%

Six types of spin solitons in three-component Bose–Einstein condensates

Wang,

Meng,

Zhao

2024

Commun. Theor. Phys.

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Exact analytical solutions are good candidates for studying and explaining the dynamics of solitons in nonlinear systems. We further extend the region of existence of spin solitons in the nonlinearity coefficient space for the spin-1 Bose-Einstein condensate. Six types of spin soliton solutions can be obtained and they exist in different regions. Stability analysis and numerical simulation results indicate that three types of spin solitons are stable against weak noise. The non-integrable properties of the model can induce shape oscillation and increase in speed after the collision between two spin solitons. These results further enrich the soliton family for non-integrable models and can provide theoretical references for experimental studies.

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Section: Constraint Conditionsmentioning

confidence: 99%

Six types of spin solitons in three-component Bose–Einstein condensates

Wang,

Meng,

Zhao

2024

Commun. Theor. Phys.

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“…, and inserting the expansions of P + into (6a). Then comparing the same order terms of λ , the potential matrix Q can be given by Q = −i Λ , P [1] + = i Λ , P [1] − (14) and the coefficient of λ −1 : P [1] +,x = i[λ , P [2] + ] + QP [1] + , P [1] −,x = i[λ , P [2] − ] − P [1] − Q. Then together with the equations ( 14), we can conclude that the asymptotic expansion of…”

Section: Riemann-hilbert Problemmentioning

confidence: 99%

“…Due to the important application in nonlinear optics, abundant optical solitons [6][7][8][9][10][11] and some new exact solutions [12] for LPD equation were explored. Besides, the rich dynamic behaviors of solitons, rogue waves and the interactional solutions for a multi-component LPD equation were studied by Darboux transformation [13][14][15][16] and inverse scattering method [17].…”

Section: Introductionmentioning

confidence: 99%

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

Wang

Chen

2022

Nonlinear Dyn

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The inverse scattering transformation for a novel nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann-Hilbert problem. Firstly, a novel integrable nonlocal LPD equation corresponding to a 3 × 3 Lax pair is proposed. Secondly, the inverse scattering process with a novel left-right 3 × 3 matrix Riemann-Hilbert(RH) problem is constructed. The analytical properties and symmetry relations for the Jost functions and scattering data, which are considerably different from the local ones. Due to the special symmetry properties for the nonlocal LPD equation, the zeros of the RHP problem are purely imaginary or occur in pairs. With different types and configuration of zeros, the soliton formula are provided and the rich dynamical behaviors for the three kinds of multi-solitons for the novel nonlocal LPD equation are demonstrated. Third, by a technique of adding perturbed parameters and limiting process, the formula of higher-order solitons for the nonlocal LPD equation is exhibited. Lastly, the plots of diverse higher-order solitons and various solutions corresponding to different combinations of the following zeros: purely imaginary higher-order zeros, purely imaginary simple zeros, pairs of non-purely imaginary simple zeros and pairs of non-purely imaginary higher-order zeros are displayed.

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Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

Guo

2022

Annalen der Physik

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Nonlinear waves on periodic backgrounds play an important role in physical systems. In this study, nonlinear waves that include solitons, breathers, rogue waves, and semi-rational solutions on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations are investigated. Moreover, the interactions between different types of nonlinear waves are examined and their dynamic behaviors are studied. In particular, it is observed that bright-dark rogue waves interact with bright-dark breathers or solitons on periodic backgrounds, four-petaled breathers interact with two eye-shaped breathers on periodic backgrounds, and a four-petal rogue wave interplays with a rogue wave on periodic backgrounds. Furthermore, it is found that the value of the parameter 𝜸 3 affects the weak and strong interactions of these nonlinear waves. These results may be useful in the study of nonlinear wave dynamics in coupled nonlinear wave models.

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Strong and weak interactions of rational vector rogue waves and solitons to anyn-component nonlinear Schrödinger system with higher-order effects

Cited by 6 publications

References 78 publications

Six types of spin solitons in three-component Bose–Einstein condensates

Six types of spin solitons in three-component Bose–Einstein condensates

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

Interactions of Localized Wave Structures on Periodic Backgrounds for the Coupled Lakshmanan–Porsezian–Daniel Equations in Birefringent Optical Fibers

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