Refraction of dispersive shock waves

@article{El2011RefractionOD,
  title={Refraction of dispersive shock waves},
  author={Gennady A. El and V. V. Khodorovskii and A. M. Leszczyszyn},
  journal={Physica D: Nonlinear Phenomena},
  year={2011},
  volume={241},
  pages={1567-1587}
}

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References

SHOWING 1-10 OF 76 REFERENCES

Interactions of dispersive shock waves

Resolution of a shock in hyperbolic systems modified by weak dispersion.

  • G. El
  • Mathematics
    Chaos
  • 2005
We present a way to deal with dispersion-dominated "shock-type" transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic

Dispersive and classical shock waves in Bose-Einstein condensates and gas dynamics

A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock-wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a

Piston dispersive shock wave problem.

In this work, the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schrödinger equation is analyzed and asymptotic solutions are calculated for a piston moving with uniform speed into a dispersive fluid at rest.

Dissipationless shock waves in media with positive dispersion

We consider nonstationary one-dimensional flows in dissipationless hydrodynamics with positive dispersion which is described by the nonlinear Schrodinger equation. We determine the conditions for the

Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.

Good agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham

Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle.

An extension of the traditional modulation description of DSWs to include the linear "ship-wave" pattern forming outside the nonlinear modulation region of the front DSW, which is relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

Generation of undular bores in the shelves of slowly-varying solitary waves.

The nonlinear evolution of the shelves is described in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants, which describe the generation of small "secondary" solitary waves in the trailing shelves.

Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston

The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow
...