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- Korteweg–De Vries equation - Wikipedia
In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces
- The Korteweg-de Vries Equation: History, exact Solutions, and . . .
This is the Korteweg-de Vries Equation (KdV) which is nonlinear because of the product shown in the second summand and which is of third order because of the third derivative as highest in the third summand
- Equations of KdV type - UCLA Mathematics
It is known that solutions to the completely integrable equations (i e KdV and mKdV) always resolve to a superposition of solitons as t -> infinity, but it is an interesting open question as to whether the same phenomenon occurs for the other KdV -type equations
- Korteweg-de Vries Equation -- from Wolfram MathWorld
Lax (1968) showed that the KdV equation is equivalent to the so-called "isospectral integrability condition" for pairs of linear operators, known as Lax pairs (Tabor 1989, p 304)
- The History and Significance of the KdV Equation
Shortly after that, another remarkable discovery was made concerning the KdV equation A paper by C Gardner, J Greene, M Kruskal, and R Miura demonstrated that it was possible to write many exact solutions to the equation by using ideas from scattering theory
- Korteweg–de Vries Equation (KdV), History, Exact N-Soliton . . .
The identification of the KdV equation as an isospectral flow of the Schrödinger operator enabled GGKM to devise a method of solving the KdVequation (with 'rapidly decreasing' boundary conditions), called the inverse scattering or inverse spectral transform (IST)
- Korteweg-de Vries equation - Encyclopedia of Mathematics
This whole procedure of solving the KdV-equation is known as the inverse spectral-transform method (IST-method, inverse-scattering method), and it can be seen as a non-linear analogue of the Fourier-transform method for solving linear partial differential equations with constant coefficients
- The KdV Equation and Solitons - doc. comsol. com
The Korteweg-de Vries (KdV) equation, formulated in 1895 by Korteweg and de Vries, models water waves It contrasts sharply to the Burgers equation because it introduces no dissipation and the waves travel seemingly forever
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