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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Book ChapterDOI
Integrable Systems and Factorization Problems
TL;DR: The main goal of the Faro International Summer School on Factorization and Integrable Systems (FISH) was to bridge the gap between different branches of Mathematical analysis.
Journal ArticleDOI
Conservations laws and solitary wave solutions for generalized Schamel equations
Frank Verheest,Willy Hereman +1 more
TL;DR: In this paper, the solitary wave solution is given for nonlinear equations, generalizing the standard and modified Korteweg-de Vries and Schamel equations, as recently investigated by Xiao.
Journal ArticleDOI
Transmutations of supersymmetry through soliton scattering, and self-consistent condensates
TL;DR: In this paper, the authors considered the two most general families of (1+1)D Dirac systems with transparent scalar potentials, and two related families of the paired reflectionless Schrodinger operators.
Journal ArticleDOI
Analyticity of solutions of the generalized Korteweg-De Vries equation with respect to their initial values
TL;DR: In this article, it was shown that the initial value problem of the generalized Korteweg-de Vries (KdV) equation is Frechet differentiable and analytic.
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