Dispersive Shock Waves in Nonlinear Arrays

Jia, Shu; Wan, Wenjie; Fleischer, Jason W.

doi:10.1103/physrevlett.99.223901

Cited by 62 publications

(48 citation statements)

References 22 publications

(24 reference statements)

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“…Even if the link to superfluidity is rarely made in explicit terms, nonlinear-tunneling experiments similar to the one we are proposing have been recently performed by several groups [42][43][44].…”

Section: Stationary Intensity Profilesmentioning

confidence: 99%

Optomechanical signature of a frictionless flow of superfluid light

Larré

Carusotto

2015

Phys. Rev. A

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We propose an experimental setup that should make it possible to reveal the frictionless flow of a superfluid of light from the suppression of the drag force that it exerts onto a material obstacle. In the paraxialpropagation geometry considered here, the photon-fluid dynamics is described by a wave equation analogous to the Gross-Pitaevskii equation of dilute Bose-Einstein condensates and the obstacle consists in a solid dielectric slab immersed into a nonlinear optical liquid. By means of an ab initio calculation of the electromagnetic force experienced by the obstacle, we anticipate that superfluidity is detectable in state-of-the-art experiments from the disappearance of the optomechanical deformation of the obstacle.

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Section: Stationary Intensity Profilesmentioning

confidence: 99%

Optomechanical signature of a frictionless flow of superfluid light

Larré

Carusotto

2015

Phys. Rev. A

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“…But here, where c 0, the transmission coefficient does depends on time; this dependance when |λ| < c, λ ∈ R is not pure phase. The associated GLM integral equation -see appendix B for a derivation -is G(x, y; t) + Ω(x + y; t) + ∞ x Ω(y + z; t)G(x, z; t) dz = 0, (9) where…”

Section: Ist Solutionmentioning

confidence: 99%

“…Dispersive shock waves (DSWs) have been seen in plasmas [1], fluids (e.g., undular bores) [2,3], superfluids [4][5][6][7], and optics [8][9][10][11]. DSWs occur when weak nonlinearity and weak dispersion dominate the physics and there is step-like data.…”

Section: Introductionmentioning

confidence: 99%

Dispersive shock wave interactions and asymptotics

Ablowitz

Baldwin

2013

Phys. Rev. E

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Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, step-like data is a single-phase DSW; this DSW is the 'largest' possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multi-step data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time.

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“…Dispersive shock waves (DSWs) appear when dispersion dominates dissipation for step-like data; they have been seen in plasmas [1], fluids (e.g., undular bores) [2,3], superfluids [4,5,6,7], and optics [8,9,10,11]. The Korteweg-de Vries (KdV) equation is the leading-order asymptotic equation for weakly dispersive and weakly nonlinear systems [12].…”

Section: Introductionmentioning

confidence: 99%

Interactions and asymptotics of dispersive shock waves – Korteweg–de Vries equation

Ablowitz

Baldwin

2013

Physics Letters A

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The long-time asymptotic solution of the Korteweg-deVries equation for general, step-like initial data is analyzed. Each sub-step in well-separated, multi-step data forms its own single dispersive shock wave (DSW); at intermediate times these DSWs interact and develop multiphase dynamics. Using the inverse scattering transform and matched-asymptotic analysis it is shown that the DSWs merge to form a single-phase DSW, which is the 'largest' one possible for the boundary data. This is similar to interacting viscous shock waves (VSW) that are modeled with Burgers' equation, where only the single, largest-possible VSW remains after a long time.

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Dispersive Shock Waves in Nonlinear Arrays

Cited by 62 publications

References 22 publications

Optomechanical signature of a frictionless flow of superfluid light

Optomechanical signature of a frictionless flow of superfluid light

Dispersive shock wave interactions and asymptotics

Interactions and asymptotics of dispersive shock waves – Korteweg–de Vries equation

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