Journal ArticleDOI
Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
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This article is published in Functional Analysis and Its Applications.The article was published on 1979-07-01. It has received 815 citations till now. The article focuses on the topics: Inverse scattering problem & Quantum inverse scattering method.read more
Citations
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Lie algebras and equations of Korteweg-de Vries type
TL;DR: A survey of the theory of Kats-Moody algebras is given in this paper, which contains a description of the connection between the infinite-dimensional Lie algebra of Kats and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the inverse scattering problem.
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Loop groups and equations of KdV type
Graeme Segal,George Wilson +1 more
TL;DR: In this article, the authors decrit une construction qui attribue une solution de l'equation de Korteweg-de Vries a chaque point d'un certain grassmannien de dimension infinie.
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Dressing transformations and Poisson group actions
TL;DR: In this paper, les proprietes de Poisson explique les transformations d'habillage en theorie des solitons, and explique le transformation of a homonym.
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The reduction problem and the inverse scattering method
TL;DR: In this article, the problem of reduction for systems of nonlinear equations integrable by the inverse scattering method is discussed and an infinite set of conservation laws is constructed for the system of equations for a two-dimensional Toda chain, the inverse problem is solved and exact N-soliton solutions are found.
References
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Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Book
Integrals of Nonlinear Equations of Evolution and Solitary Waves
TL;DR: In this article, a general principle for associating nonlinear equations evolutions with linear operators so that the eigenvalues of the linear operator integrals of the nonlinear equation can be found is presented, where the main tool used is the first remarkable series of integrals discovered by Kruskal and Zabusky.
Journal ArticleDOI
Integrable Hamiltonian systems and interactions through quadratic constraints
TL;DR: In this article, the relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems.
Journal ArticleDOI
A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
Journal ArticleDOI
Nonlinear evolution equations solvable by the inverse spectral transform.—I
TL;DR: In this paper, a class of nonlinear evolution equations solvable by the inverse spectral transform (IST) was introduced, which is more general than that introduced by Ablowitz, Kaup, Newell and Segur and includes equations involving more than one space variable and containing coefficients that are not constant.