5 citations
3 papers
math.AP2013★ 5 cited
Solution of the KdV equation on the line with analytic initial potential
Andrey Melnikov
We present a theory of Sturm-Liouville non-symmetric vessels, realizing an inverse scattering theory for the Sturm-Liouville operator with analytic potentials on the line. This con…
math.FA2012★ 2 cited
Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrant
Andrey Melnikov
Using Gelfand-Levitan theory on a half line, we construct a vessel for the class of potentials, whose spectral functions satisfy a certain regularity assumption. When the singular…
math.AP2012★ 5 cited
On construction of solutions of evolutionary Non Linear Schrodinger equation
A. Melnikov
In this work we present an application of a theory of vessels to solution of the evolutionary Non Liner Schrodinger (NLS) equation. The classes of functions for which the initial v…