scispace - formally typeset

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). more


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 more

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

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

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

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

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

1,707 Citations

No. of papers in the topic in previous years

Top Attributes

Show by:

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

Network Information
Related Topics (5)

25.2K papers, 516.1K citations

94% related
Dissipative system

21.8K papers, 440.2K citations

90% related
Schrödinger equation

25.5K papers, 535.4K citations

89% related
Hamiltonian system

14.1K papers, 313.7K citations

89% related
Partial differential equation

70.8K papers, 1.6M citations

89% related