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Nonlinear Schrödinger equation

About: Nonlinear Schrödinger equation is a(n) research topic. Over the lifetime, 12704 publication(s) have been published within this topic receiving 296760 citation(s).

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Papers
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Open accessJournal ArticleDOI: 10.1115/1.3423786
G. B. Whitham, T. C. T. Ting1Institutions (1)
Abstract: Keywords: ondes ; chocs ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08

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Topics: Wave propagation (72%), Mechanical wave (70%), Lamb waves (69%) ...read more

4,773 Citations


Open accessBook
01 Jan 1987-
Abstract: The Nonlinear Schrodinger Equation (NS Model)- Zero Curvature Representation- The Riemann Problem- The Hamiltonian Formulation- General Theory of Integrable Evolution Equations- Basic Examples and Their General Properties- Fundamental Continuous Models- Fundamental Models on the Lattice- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models- Conclusion- Conclusion

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Topics: Nonlinear Schrödinger equation (56%), Integrable system (56%), Riemann problem (55%) ...read more

2,417 Citations


Open accessPosted Content
Abstract: The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models. Heisenberg Antiferromagnet and Hubbard models. It is explained in detail, how to calculate correlation functions.

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Topics: Bethe ansatz (80%), Quantum inverse scattering method (69%), Ansatz (67%) ...read more

2,092 Citations


Journal ArticleDOI: 10.1038/NATURE06402
13 Dec 2007-Nature
Abstract: Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrodinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

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Topics: Optical rogue waves (81%), Rogue wave (65%), Peregrine soliton (54%) ...read more

1,854 Citations


Open accessBook
01 Jun 1982-
Abstract: A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.

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Topics: Nonlinear Schrödinger equation (67%), Inverse scattering transform (67%), Soliton (66%) ...read more

1,707 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202231
2021746
2020632
2019693
2018590
2017676

Top Attributes

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Topic's top 5 most impactful authors

Boris A. Malomed

133 papers, 4K citations

Anjan Biswas

64 papers, 2.5K citations

Rémi Carles

61 papers, 1.2K citations

Aly R. Seadawy

60 papers, 2.1K citations

Nail Akhmediev

55 papers, 3.9K citations

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