The Physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: Rogue waves, modulation instability and self-focusing phenomena

Reviews in Physics ◽

10.1016/j.revip.2019.100037 ◽

2020 ◽

Vol 5 ◽

pp. 100037 ◽

Author(s):

François Copie ◽

Stéphane Randoux ◽

Pierre Suret

Keyword(s):

Schrödinger Equation ◽

Fiber Optics ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulation Instability ◽

Rogue Waves ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Self Focusing ◽

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Bifurcation structures and dominant modes near relative equilibria in the one-dimensional discrete nonlinear Schrödinger equation

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2009.01.001 ◽

2009 ◽

Vol 238 (6) ◽

pp. 687-698 ◽

Author(s):

C.L. Pando L. ◽

E.J. Doedel

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Relative Equilibria ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

The One ◽

Bifurcation Structures

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A Collective Coordinate Approach to the One-Dimensional Nonlinear Schrödinger Equation with Spatial Periodic Potentials

NATO ASI Series - Future Directions of Nonlinear Dynamics in Physical and Biological Systems ◽

10.1007/978-1-4899-1609-9_14 ◽

1993 ◽

pp. 85-96

Author(s):

A. R. Bishop ◽

Rainer Scharf

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Periodic Potentials ◽

Collective Coordinate ◽

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Periodic standing waves in the focusing nonlinear Schrödinger equation: Rogue waves and modulation instability

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2020.132378 ◽

2020 ◽

Vol 405 ◽

pp. 132378 ◽

Author(s):

Jinbing Chen ◽

Dmitry E. Pelinovsky ◽

Robert E. White

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulation Instability ◽

Standing Waves ◽

Rogue Waves ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Periodic Standing Waves

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Exact form of the Bogolyubov excitations in the one-dimensional nonlinear Schrödinger equation

Physics Letters A ◽

10.1016/s0375-9601(01)00467-4 ◽

2001 ◽

Vol 287 (3-4) ◽

pp. 273-277 ◽

Author(s):

D.L. Kovrizhin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

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Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity

Physical Review A ◽

10.1103/physreva.62.063610 ◽

2000 ◽

Vol 62 (6) ◽

Author(s):

L. D. Carr ◽

Charles W. Clark ◽

W. P. Reinhardt

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Stationary Solutions ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

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Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with an external potential

Physical Review A ◽

10.1103/physreva.76.013612 ◽

2007 ◽

Vol 76 (1) ◽

Author(s):

Xiao-Yan Tang ◽

Padma Kant Shukla

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

External Potential ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Spatially Inhomogeneous ◽

The One ◽

Quintic Nonlinear Schrödinger Equation

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Decaying steady states of the one-dimensional nonlinear Schrödinger equation with a constant potential

Journal of Physics Conference Series ◽

10.1088/1742-6596/792/1/012031 ◽

2017 ◽

Vol 792 ◽

pp. 012031 ◽

Author(s):

G Torres-Vega

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Steady States ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Constant Potential ◽

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Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials

Physical Review E ◽

10.1103/physreve.47.1375 ◽

1993 ◽

Vol 47 (2) ◽

pp. 1375-1383 ◽

Author(s):

Rainer Scharf ◽

A. R. Bishop

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Length Scale ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

Periodic Potentials ◽

Spatially Periodic ◽

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Barrier transmission for the one-dimensional nonlinear Schrödinger equation: Resonances and transmission profiles

Physical Review A ◽

10.1103/physreva.77.063610 ◽

2008 ◽

Vol 77 (6) ◽

Author(s):

K. Rapedius ◽

H. J. Korsch

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

One Dimensional ◽

Nonlinear Schrödinger ◽

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Vector rogue waves, rogue wave-to-soliton conversions and modulation instability of the higher-order matrix nonlinear Schrödinger equation

The European Physical Journal Plus ◽

10.1140/epjp/i2018-12282-8 ◽

2018 ◽

Vol 133 (12) ◽

Author(s):

Wen-Rong Sun ◽

Lei Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulation Instability ◽

Rogue Waves ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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