Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators

Ablowitz, Mark J.; Cole, Justin T.; Hu, Pipi; Rosenthal, P.

doi:10.1103/physreve.103.042214

Cited by 10 publications

(8 citation statements)

References 35 publications

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“…Indeed, it has been argued in recent works, including Refs. [30,31,38], that topology may control and, indeed, even enhance (when suitably leveraged) the mobility of states that might not be otherwise particularly mobile (e.g., due to Peierls-Nabarro and associated barriers [31,33]) in conventional discrete settings. It is intriguing to consider if mobility of photonic modes can be achieved in a similar way to what is seen in the propagation of nonlinear elastic waves in flexible structures, which provides opportunities for locomotion of mechanical robots [39].…”

Section: Conclusion and Future Challengesmentioning

confidence: 99%

“…Features such as the uninhibited unidirectional, scatter-free (around lattice defects) propagation of nonlinear edge modes in topological lattices (such as Lieb, Kagomé, etc.) [30], as well as the absence of Peierls-Nabarro, discreteness-induced barriers in nonlinear Floquet topological insulators [31] have been manifested. These suggest the particular promise of topological nonlinear media in overcoming some of the limitations of conventional nonlinear modes.…”

Section: Introductionmentioning

confidence: 99%

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Floquet solitons in square lattices: Existence, stability, and dynamics

et al. 2022

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In the present work, we revisit a recently proposed and experimentally realized topological two-dimensional lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon an oscillation period of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multisoliton analogs of these Floquet states, inspired by the corresponding discrete nonlinear Schrödinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again analogously to their DNLS counterparts.

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Section: Conclusion and Future Challengesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Floquet solitons in square lattices: Existence, stability, and dynamics

et al. 2022

View full text Add to dashboard Cite

show abstract

“…Another aspect in which topological features may have a strong imprint is the mobility of nonlinear modes. Indeed, it has been argued in recent works, including [30,31,34] that topology may control and, indeed, even enhance (when suitably leveraged) the mobility of states that might not be otherwise particularly mobile (e.g., due to Peierls-Nabarro and associated barriers [31,33]) in conventional discrete settings. It is intriguing to consider if mobility of photonic modes can be achieved in a similar way seen in the propagation of nonlinear elastic waves in flexible structures which provides opportunities for locomotion of mechanical robots [35].…”

Section: Conclusion and Future Challengesmentioning

confidence: 99%

“…Features such as the uninhibited unidirectional, scatter-free (around lattice defects) propagation of nonlinear edge modes in topological lattices (such as Lieb, Kagomé etc.) [30], as well as the absence of Peierls-Nabarro, discretenessinduced barriers in nonlinear Floquet topological insulators [31] have been manifested. These suggest the particular promise of topological nonlinear media in overcoming some of the limitations of "conventional" nonlinear modes.…”

Section: Introductionmentioning

confidence: 99%

Floquet solitons in square lattices: Existence, Stability and Dynamics

Parker,

Cuevas-Maraver,

Kevrekidis

et al. 2021

Preprint

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In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon a period oscillation of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multi-soliton analogues of these Floquet states, inspired by the corresponding discrete nonlinear Schrödinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again in analogy to their DNLS counterparts.

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“…This equation is a different fractional generalization of the IDNLS equation in which the linear second order difference is replaced by the discrete fractional Laplacian [37][38][39][40]. The fADNLS equation can be understood as a discretization of a fractional NLS equation involving the Riesz derivative which has been extensively studied in, e.g., [41][42][43][44][45]; it is also is also closely related to the (likely) non-integrable fractional DNLS equation, recently studied in [37,46]. Though the fADNLS equation is likely not integrable to our knowledge (apart from the limiting case when fADNLS reduces to IDNLS), the similarity between the two equations suggests that some of the physical predictions of fractional integrable equations are shared by equations which are simpler to realize computationally.…”

Section: Introductionmentioning

confidence: 99%

Fractional Integrable and Related Discrete Nonlinear Schrödinger Equations

Ablowitz¹,

Been²,

Carr³

2022

Preprint

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Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schrödinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential difference equation of this type is found, the fractional integrable discrete nonlinear Schrödinger equation. This equation is linearized; special soliton solutions are found whose peak velocities exhibit more complicated behavior than other previously obtained fractional integrable equations. This equation is compared with the closely related fractional averaged discrete nonlinear Schrödinger equation which has simpler structure than the integrable case. For positive fractional parameter and small amplitude waves, the soliton solutions of the integrable and averaged equations have similar behavior.

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Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators

Cited by 10 publications

References 35 publications

Floquet solitons in square lattices: Existence, stability, and dynamics

Floquet solitons in square lattices: Existence, stability, and dynamics

Floquet solitons in square lattices: Existence, Stability and Dynamics

Fractional Integrable and Related Discrete Nonlinear Schrödinger Equations

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