Journal ArticleDOI
Korteweg-devries equation and generalizations. VI. methods for exact solution
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1974-01-01. It has received 796 citations till now. The article focuses on the topics: Exact differential equation.read more
Citations
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Supersymmetry and quantum mechanics
TL;DR: In this article, the authors review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications, including shape invariance and operator transformations, and show that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials.
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Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
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A Simple model of the integrable Hamiltonian equation
TL;DR: In this paper, a method of analysis of the infinite-dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested, based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equation with their symmetries by using symplectic operators.
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The soliton: A new concept in applied science
TL;DR: The term soliton has been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed.
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Three integrable Hamiltonian systems connected with isospectral deformations
TL;DR: In this paper, three integrable hamiltonian systems connected with isospectral deformations are discussed, where wave solutions of a nonlinear partial differential equation have a strong stability behavior.
References
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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
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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
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XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
D. J. de Korteweg,G. de Vries +1 more
TL;DR: In this article, the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves were discussed, and a new model of long wave propagation was proposed.
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Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.
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.