Localized Modes in Nonlinear Fractional Systems with Deep Lattices

Liu, Xiuye; Malomed, Boris A.; Zeng, Jianhua

doi:10.1002/adts.202100482

Cited by 16 publications

(2 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The stationary solutions of non-linear Schrödinger equation have always been an interesting field. Therefore, when the non-linear Schrodinger equation is expanded from the standard integer order to the fractional order, that is non-linear fractional Schrödinger equation(NLFSE), many intriguing localized states/modes were revealed, including spatial solitons supported by PT-symmetry, symmetric and antisymmetric solitons, fundamental solitons, multipole gap solitons, discrete vortex solitons, vortex solitons and gap solitons and so forth in Kerr nonlinearity [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

Zhou

Zeng²,

Qin³

2023

Front. Phys.

Self Cite

View full text Add to dashboard Cite

We investigate the existence and stability of localized gap states at a non-linear interface of non-linear fractional systems in a one-dimensional photonic lattice. By using the direct numerical simulations and linear stability analysis, we obtain the stability of the asymmetric localized gap states in the first and second finite gaps. Our theoretical results show that the power of the localized gap states decrease gradually as the increase of propagation constant and the non-linear landscape (non-linear coefficient ratio between the left and right interface), providing insights into soliton physics in non-linear periodic systems with fractional-order diffraction.

show abstract

Section: Introductionmentioning

confidence: 99%

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

Zhou

Zeng²,

Qin³

2023

Front. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Besides, the PT-symmetric periodic potential [50] was also introduced to the FNLS equation [51] such that stable one- and two-dimensional localized modes were found in such models even if the corresponding linear PT-phase was broken. The vortex solitons were also proven to exist in the two-dimensional FNLS equation with optical lattices [52,53].…”

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.

View full text Add to dashboard Cite

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.

show abstract

Two-dimensional localized modes in nonlinear systems with linear nonlocality and moiré lattices

Liu,

Zeng

2024

Front. Phys.

View full text Add to dashboard Cite

Localized Modes in Nonlinear Fractional Systems with Deep Lattices

Cited by 16 publications

References 93 publications

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

Asymmetric localized states at a nonlinear interface of fractional systems with optical lattices

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

Two-dimensional localized modes in nonlinear systems with linear nonlocality and moiré lattices

Contact Info

Product

Resources

About