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
Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chain
TL;DR: In this paper, the authors examined and obtained analytic expressions for the basic nonlinear excitations in a monoatomic chain with cubic and quartic interatomic potentials and verified their stability under collision.
Journal ArticleDOI
The recursion operator of the Kadomtsev-Petviashvili equation and the squared eigenfunctions of the Schrödinger operator
TL;DR: On deduit, grâce a un algorithme, l'operateur de recurrence de l'equation de Kadomtsev-Petviashvili as mentioned in this paper.
Journal ArticleDOI
Positons: Slowly Decreasing Analogues of Solitons
TL;DR: In this article, the authors presented an introduction to positon theory, almost never covered in the Russian scientific literature, and constructed soliton-positon solutions of the KdV equation for the Toda chain, the NS equation, as well as the sinh-Gordon equation and its lattice analogue.
Journal ArticleDOI
On the symmetries of evolution equations
TL;DR: In this paper, the authors introduce the notion of finite dimensionality of classical symmetries and define subalgebras of K3 and differential substitutions for systems of evolution equations.
Book ChapterDOI
The Generation and Propagation of Oscillations in Dispersive Initial Value Problems and Their Limiting Behavior
TL;DR: In this paper, the authors review a variety of equations describing physical systems in which dissipative or diffusive mechanisms are absent, but which undergo dispersive processes, and investigate the limiting behavior of such a system when the parameter in the dispersive term tends to zero.
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