Journal ArticleDOI
Method for solving the Korteweg-deVries equation
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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
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Journal ArticleDOI
Internal solitons in the andaman sea.
A. R. Osborne,T. L. Burch +1 more
TL;DR: Using theoretical results from the physics of nonlinear waves, it is shown that the internal waves are solitons and their interactions with surface waves are described.
Journal ArticleDOI
The Stability of Solitary Waves
TL;DR: In this article, it was shown that the Kortewegde-de-vries equation is invariant with time, and the stability of the solution of this equation is established.
Journal ArticleDOI
Long Nonlinear Internal Waves
TL;DR: In this paper, an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example.
Journal ArticleDOI
Non-linear equations of korteweg-de vries type, finite-zone linear operators, and abelian varieties
TL;DR: In this paper, 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.
Book ChapterDOI
Direct Methods in Soliton Theory
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.
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