Modulation instability: The beginning

By V. Zakharov, L. Ostrovsky. 2009

784 citations recorded by the source corpus.

Subfields: Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a6fa556c338fb3271506559cc46ae197fa7ef13

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In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Fibre multi-wave mixing combs reveal the broken symmetry of Fermi–Pasta–Ulam recurrence (2018, background): “In particular, in optical fibres where the propagation is ruled by the nonlinear Schrödinger equation (NLSE), FPU recurrence is triggered by the universal phenomenon of MI [4], i.”
Dispersive shock waves and modulation theory (2016, background): “Although many dispersive hydrodynamic systems exhibit hyperbolic Whitham equations, when the Whitham equations are of elliptic type, the initial value problem is ill-posed and nonlinear wavetrains exhibit modulational instability [69, 70, 1, 71].”
Hybrid photonic-crystal fiber (2017, background): “…contained the fewest spatiotemporal modes, a requirement 37 For a description of this process in conventional optical fibers see the literature following the first proposal (Hasegawa and Brinkman, 1980), demonstration (Tai et al., 1986), or early history in general (Zakharov and Ostrovsky, 2009).”
Instabilities, breathers and rogue waves in optics (2014, background): “ AND BREATHER DYNAMICS Modulation instability is a fundamental property of many nonlinear dispersive systems, associated with the growth of periodic perturbations on a continuous wave (CW) background [16]. In the initial evolution, the spectral sidebands associated with the instability experience ex”
Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation (2015, background): “Recently, several reported experiments were related to the modulational instability (MI) and the breather solution of the NLS equation in nonlinear optics [3,4].”
Rogue waves and their generating mechanisms in different physical contexts (2013, background): “Themodulational instability, also known as the Benjamin–Feir instability, has been discovered in thewater wave context in the late sixties independently by Benjamin and Feir [48] and Zakharov [49]; see [50] for an historical review on the subject and possible applications.”
Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants (2019, neutral): “q2k−1 = Ωk + ωk 2 , q2k = Ωk − ωk 2 , ξ0 2k−1 = ξ 0 2k = ξ 0 k , η 0 2k−1 = η 0 2k = η 0 k , (13)”