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Nonlinear Schrödinger equation

About: Nonlinear Schrödinger equation is a research topic. Over the lifetime, 12704 publications have been published within this topic receiving 296760 citations.


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Journal ArticleDOI
TL;DR: In this paper, a reference record was created on 2005-11-18, modified on 2016-08-08 and used for the purpose of ondes ; chocs ; onde de : choc reference record.
Abstract: Keywords: ondes ; chocs ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08

4,774 citations

Book
01 Jan 1987
TL;DR: The Nonlinear Schrodinger Equation (NS Model) and Zero Curvature Representation (ZCR) as discussed by the authors have been used for the classification and analysis of Integrable Evolution Equations.
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

2,539 citations

Journal ArticleDOI
13 Dec 2007-Nature
TL;DR: This work reports 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.
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.

2,173 citations

Posted Content
TL;DR: In this article, a detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well as main models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.
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.

2,160 citations

Book
01 Jun 1982
TL;DR: A discussion of the theory and applications of classical solitons is presented in this paper with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory, including solitary waves and soliton, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation.
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.

1,707 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023208
2022470
2021754
2020634
2019694
2018590