Journal ArticleDOI
Method for solving the Korteweg-deVries equation
Reads0
Chats0
TLDR
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 asAbstract:
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 $|x|\ensuremath{\rightarrow}\ensuremath{\infty}$. The method can be used to predict exactly the "solitons," or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.read more
Citations
More filters
Journal ArticleDOI
The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation
TL;DR: A detailed analysis of the cubic Schrodinger equation under the boundary conditions as |x|→∞ is given in this paper, where the inverse-scattering technique is used, and the asymptotic state is a series of solitons.
Journal ArticleDOI
The Korteweg–deVries Equation: A Survey of Results
TL;DR: A survey of results for the Korteweg-deVries equation can be found in this paper, including conservation laws, an alternate method for exact solution, soliton solutions, asymptotic behavior of solutions, Backlund transformation, and a nonlinear WKB method.
Book
Inverse Sturm-Liouville problems and their applications
TL;DR: Inverse spectral problems for Sturm-Liouville differential operators are studied in this paper, where the authors present the main results and methods on inverse spectral problems and their applications.
Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)
TL;DR: In this article, the authors present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations, which they solve exactly using a kind of perturbational approach.
Non-linear equations of korteweg-de vries type, finite-zone linear operators, and
Abelian Varieties,V. B. Matveev +1 more
TL;DR: In this article, a broad class of periodic and almost-periodic solutions of non-linear equations of mathematical physics to which (in the rapidly decreasing case) the method of the inverse scattering problem is applicable is presented.
Related Papers (5)
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
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