Journal ArticleDOI
A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
About:
This article is published in Functional Analysis and Its Applications.The article was published on 1975-01-01. It has received 875 citations till now. The article focuses on the topics: Inverse scattering problem & Inverse scattering transform.read more
Citations
More filters
Journal ArticleDOI
A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II
TL;DR: The connection between nonlinear partial differential equations solvable by inverse scattering transforms and nonlinear ODEs of P-type (i.e., no movable critical points) is discussed in this article.
Journal ArticleDOI
The quantum method of the inverse problem and the heisenberg xyz model
TL;DR: In this article, the six-vertex model is used to generate vectors and permutation relations for a two-dimensional lattice and quantum mechanics on a chain, and the Bethe Ansatz general Bethe-Anatz method is used for the inverse problem.
Book ChapterDOI
Solitons and the Inverse Scattering Transform
TL;DR: In particular, the linear dispersive term in the Korteweg-de Vries equation prevents this from ever happening in its solution as discussed by the authors, and the instability and subsequent modulation of an initially uniform wave profile can be prevented by including dispersive effects in the shallow water theory.
MonographDOI
Bäcklund and Darboux transformations : geometry and modern applications in soliton theory
Colin Rogers,Wolfgang K. Schief +1 more
TL;DR: Backlund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory have been explored in this article, where the authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged.
References
More filters
Journal ArticleDOI
Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
Journal Article
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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
The Modified Korteweg-de Vries Equation
TL;DR: In this paper, it was shown that the N -soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the k-means soliton collision.
Journal ArticleDOI
The Exact N-Soliton Solution of the Korteweg-de Vries Equation
Miki Wadati,Morikazu Toda +1 more
TL;DR: The exact N -soliton solution of the Korteweg-de Vries equation is obtained through the procedure suggested by Gardner, Greene, Kruskal and Miura as mentioned in this paper.