Excited States of Magnetotrion

Kuznetsov, V. A.; Кулик, Л. В.; Журавлев, А. С.; Gorbunov, A. V.; Kirpichev, V. E.; Khannanov, M. N.; Кукушкин, И. В.

doi:10.1134/s0021364018020091

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…Notice that in the local limit of d = 0 (i.e., α = 1), we solely obtain the KPI model, in which line solitons are unstable: as was shown in plasma physics and hydrodynamics [20], line solitons develop undulations and eventually decay into lumps [21]. In the same venue, but now in optics, the asymptotic reduction of the defocusing 2D NLS to KPI [22,23], and the instability of the line solitons of the latter, was used to better understand the transverse instability of rectilinear dark solitons: indeed, these structures also develop undulations and eventually decay into vortex pairs [23,24].…”

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confidence: 78%

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

Horikis

Frantzeskakis

2017

Phys. Rev. Lett.

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Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in (2 + 1)-dimensions. We identify an analogue of surface tension in optics, namely a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a KadomtsevPetviashvilli (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters. 05.45.Yv, 42.65.Tg, 47.11.St, 47.35.Fg Many physically different contexts can be brought together through common modeling and mathematical description. A common (and rather unlike) example is water waves and nonlinear optics. Two models are inextricably linked with both subjects: the universal Korteweg-de Vries (KdV) and nonlinear Schrödinger (NLS) equations [1]. Furthermore, these models can be reduced from one to the other [2], thus suggesting that phenomena occurring in water waves may also exist in optics. Here, using such reductions for a nonlocal NLS, we find that surface tension -which causes fluids to minimize the area they occupy-has a direct analogue in optics.Key to our findings are solitons, i.e., robust localized waves that play a key role in numerous studies in physics [3], applied mathematics [4] and engineering [5]. A unique property of solitons is that they feature a particle-like character, i.e., they interact elastically, preserving their shapes and velocities after colliding with each other. Such elastic collisions, as well as pertinent emerging wave patterns, can sometimes be observed even in everyday life. A predominant example is the one pertaining to flat beaches: in such shallow water wave settings, two line solitons merging at proper angles give rise to patterns of X-, H-, or Y-shaped waves, as well as other more complicated nonlinear waveforms [6]. All these shallow water wave structures are actually exact analytical multi-dimensional line soliton solutions of the Kadomtsev-Petviashvilli (KP) equation (which generalizes KdV to two dimensions (2D) [1,4]) of the KPII type -a key model in the theory of shallow water waves with weak surface tension [1]. The relative equation with strong surface tension is referred to as KPI.Here we show that such patterns can also be observed in a quite different physical setting, i.e., the one related to optical beam propagation in media with a spatially nonlocal defocusing nonlinearity. Such media include thermal nonlinear optical media [7,8], partially ionized plasmas [9, 10], nematic liquid crystals [11,12], and dipolar bosonic quantum gases [13]. It is shown that approximate solutions of the nonlocal NLS model satisfy, at proper scales, equations that appear in the context of water waves: a Boussinesq or Benney-Luke (BL) [14], as well...

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confidence: 78%

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

Horikis

Frantzeskakis

2017

Phys. Rev. Lett.

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“…The statistical properties of weakly nonlinear wave systems have been thus proven to evolve through a kinetic equation for the second order moments of the wave amplitudes [10]. Many different systems such as waves in plasma [11][12][13][14], spin waves in solids [15,16], surface waves in fluids [7,8,10,17,18] and nonlinear optics [19,20] among others, have been shown to follow similar kinetic equations in the weakly nonlinear regime. Moreover, Zakharov has shown that stationary, out-of-equilibrium power-law solutions, naturally emerge from the kinetic equation [11].…”

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confidence: 99%

“…One can easily show that the divergence of the last two terms in the latter expression vanish identically. Therefore, collecting the expression obtained in (10), (12), (13) and using (14), we finally find the Kármán-Howarth-Monin relation for statistically homogenous WT in thin elastic plates…”

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confidence: 99%

Exact result in strong wave turbulence of thin elastic plates

Düring¹,

Krstulovic²

2018

Phys. Rev. E

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An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5-Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛℓ, where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

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“…As discussed in the previous section, in the 2D setting, line solitons of KP-I are unstable and decay into lumps [54]. In the context of the defocusing NLS, the snaking instability of dark soliton stripes results in their decay into vortices [55]; this effect was studied in detail also in the context of polariton superfluids [24].…”

Section: Numerical Resultsmentioning

confidence: 90%

“…In particular, as was first shown in hydrodynamics and plasma physics [38], line solitons develop undulations and eventually decay into lumps [54]. Additionally, in optics, the asymptotic reduction of the defocusing 2D nonlinear Schrödinger (NLS) equation to KP-I [51,55], and the instability of the line solitons of the latter, was used to better understand the transverse instability of rectilinear dark solitons: indeed, these structures being subject to transverse (alias "snaking") instability, also develop undulations and eventually decay into vortex pairs [51,56] or, in some cases, into 2D vorticityfree structures resembling KP lumps [46]. A recent analysis of the resulting line soliton filament dynamics can be found in Ref.…”

Section: The Kadomtsev-petviashvili-i Equationmentioning

confidence: 95%

Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids

et al. 2018

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We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke-type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves. From the KP-I model, we predict the existence of vorticity-free, weakly (algebraically) localized two-dimensional dark-lump solitons. We find that, in the presence of dissipation, dark lumps exhibit a lifetime three times larger than that of planar dark solitons. Direct numerical simulations show that dark lumps do exist, and their dissipative dynamics is well captured by our analytical approximation. It is also shown that lumplike and vortexlike structures can spontaneously be formed as a result of the transverse "snaking" instability of dark soliton stripes.

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Excited States of Magnetotrion

Cited by 3 publications

References 13 publications

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

Exact result in strong wave turbulence of thin elastic plates

Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids

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