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Full-Text Articles in Physical Sciences and Mathematics
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Conference papers
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.
On The Peakon And Soliton Solutions Of An Integrable Pde With Cubic Nonlinearities, Rossen Ivanov, Tony Lyons
On The Peakon And Soliton Solutions Of An Integrable Pde With Cubic Nonlinearities, Rossen Ivanov, Tony Lyons
Conference papers
The interest in the singular solutions (peakons) has been inspired by the Camassa-Holm (CH) equation and its peakons. An integrable peakon equation with cubic nonlinearities was first discovered by Qiao. Another integrable equation with cubic nonlinearities was introduced by V. Novikov . We investigate the peakon and soliton solutions of the Qiao equation.
Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov
Two Component Integrable Systems Modelling Shallow Water Waves, Rossen Ivanov
Conference papers
Our aim is to describe the derivation of shallow water model equations for the constant vorticity case and to demonstrate how these equations can be related to two integrable systems: a two component integrable generalization of the Camassa-Holm equation and the Kaup - Boussinesq system.