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
Integration method of the Korteweg-de Vries equation with a self-consistent source
TL;DR: In this article, it was shown that solutions rapidly decreasing with x of the Korteweg-de Vries equation with a self-consistent source can be found by the inverse scattering method for the one-dimensional Schrodinger operator on a straight line.
Journal ArticleDOI
Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method
S Y Lou,S Y Lou,Hongcai Ma +2 more
TL;DR: In this paper, a direct method was developed to find finite symmetry groups of nonlinear mathematical physics systems using the direct method for the well-known (2+1)-dimensional Kadomtsev-Petviashvili equation and the Ablowitz-Kaup-Newell-Segur system, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.
Journal ArticleDOI
Magnetic‐flux propagation on a Josephson transmission line
TL;DR: In this paper, the propagation of magnetic flux pulses along the insulating barrier of a long Josephson junction is investigated both theoretically and experimentally, and the theoretical study includes applications of both (i) the recently developed "inverse−scattering−transform method" (ISTM) to the corresponding sine−Gordon equation in characteristic (light cone) coordinates and (ii) Whitham's method (WM) of averaged Lagrangian analysis to the sine • Gordon equation in laboratory coordinates.
Journal ArticleDOI
Scylla and Charybdis observed from space
Werner Alpers,Ettore Salusti +1 more
TL;DR: In this article, an experimental evidence is presented that internal waves are generated in the Strait of Messina, which is linked to the tidal currents washing over the shallow sill within the strait.
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