Nondegenerate solitons of 2-coupled mixed derivative nonlinear Schrödinger equations

Geng, Kai-Li; Mou, Da-Sheng; Dai, Chao-Qing

doi:10.1007/s11071-022-07833-5

Cited by 94 publications

(14 citation statements)

References 37 publications

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“…There are many methods proposed in the literature for obtaining exact solutions of differential-difference equations (D Es). Examples of these methods are, Hirota method 21 , exponential function method 22,23 , square operator method 24,25 , similarity transformation method 26,27 , and neural network methods 28 . One of the effective methods for getting exact solution of D Es such as Eqs.…”

Section: Some New Soliton Solutions Of a Semi-discrete Fractional Com...mentioning

confidence: 99%

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Kader

Bialy

Nour

et al. 2023

Sci Rep

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Section: Some New Soliton Solutions Of a Semi-discrete Fractional Com...mentioning

confidence: 99%

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Kader

Bialy

Nour

et al. 2023

Sci Rep

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“…Soliton structures [1]- [3] excited in nonlinear evolutional systems [4]- [6] have given a great deal of help to deepen the understand of the physical mechanisms behind the actual phenomena in the areas of optical engineering [7]- [9], plasmas [10], mathematical physics [11,12] and Bose-Einstein condensates(BECs) [13,14]. Rogue wave also named as Peregrine structure(PS) has its amplitude larger over twice than waves on the background, and unexpectedly appears and then vanishes quickly without any sign [15,16].…”

Section: Introductionmentioning

confidence: 99%

3D bright-bright Peregrine triple-one structures in a nonautonomous partially nonlocal vector nonlinear Schr¨odinger model under a harmonic potential

Yang

Zhu

et al. 2023

Preprint

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Similar dynamical properties of coupled solitons have been heavily reported in previous literatures. This paper focuses on the different excitation management of two components for 3D bright-bright Peregrine triple-one structures in a nonautonomous partially nonlocal vector nonlinear Schr¨odinger model under a harmonic potential by contrasting the maximum accumulated time value with the the excited value for each Peregrine peak. Furthermore, the different diffraction values in two transverse directions affect the bright-bright Peregrine triple-one structure configurations and amplitude and width of the Peregrine structure. This study extends the management of rogue wave to the partially nonlocal phenomena of optical wave, matter wave and other nonlinear waves.

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“…The existence of solitons supported by the FNLS equation was investigated theoretically, such as the one-dimensional ground state solutions [32], spatiotemporal accessible solitons [33,34], gap solitons [35,36], multi-pole solitons [37][38][39] as well as vortex solitons in high dimensions [40][41][42]. Moreover, some other soliton structures [43][44][45]. An intriguing discovery is that when symmetry breaking phenomena occurred in fractional diffraction, asymmetric solitons are with complex propagation constants, which differs from that of integer-order cases [46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Formation of multi-peak gap solitons and stable excitations for double-Lévy-index and mixed fractional NLS equations with optical lattice potentials

Zhong

Yan

2023

Proc. R. Soc. A.

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In this paper, we investigate the new two-Lévy-index fractional nonlinear Schrödinger (FNLS) equations with optical lattices, where two fractional derivative terms are introduced to control the diffractions. Especially, we explore the linear Bloch bandgaps and existence of gap solitons for the two-Lévy-index mixed FNLS equations with optical lattices. We analyse the effects of different coefficients of normal and abnormal diffraction terms on bandgap structures. Families of single-, double-, triple-, as well as quadruple-peak solitons are found in the first gap with the defocusing nonlinearity while such solitons can be found in the semi-infinite gap when it turns to the focusing regime. Meanwhile, we find that the above-obtained gap solitons can be roughly divided into two types, one of which branches out from the band edge, and another one cannot branch out from the band edge. Moreover, the stability of gap solitons is discussed via the linear stability analysis, and then their dynamical behaviours are verified by means of direct simulations. And stable multi-peak solitons can be obtained via analysing the phase structure. Meanwhile, we find the stable excitations of gap solitons via excitations of system parameters. The stable gap solitons are also verified to appear in the two-Lévy-index FNLS equation. These results may pave the way for the study of linear and nonlinear phenomena of two-Lévy-index and mixed FNLS equations or other mixed fractional physical models in optical lattices and the related physical experimental designs.

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Nondegenerate solitons of 2-coupled mixed derivative nonlinear Schrödinger equations

Cited by 94 publications

References 37 publications

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

3D bright-bright Peregrine triple-one structures in a nonautonomous partially nonlocal vector nonlinear Schr¨odinger model under a harmonic potential

Formation of multi-peak gap solitons and stable excitations for double-Lévy-index and mixed fractional NLS equations with optical lattice potentials

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