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Full-Text Articles in Physical Sciences and Mathematics
Dark Solitons Of The Qiao's Hierarchy, Rossen Ivanov, Tony Lyons
Dark Solitons Of The Qiao's Hierarchy, Rossen Ivanov, Tony Lyons
Articles
We obtain a class of soliton solutions of the integrable hierarchy which has been put forward in a series of works by Z. Qiao. The soliton solutions are in the class of real functions approaching constant value fast enough at infinity, the so-called 'dark solitons'.
Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons
Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons
Articles
We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a Z2 reduction group. The soliton solutions are explicitly obtained.