Search academic texts

Information × Registration Number 0223U000174, 0121U111968 , R & D reports Title Nonstandard nonlocal and peakon integrable equations: asymptotics and inverse scattering transform popup.stage_title Head Filipkovska Mariia S., Кандидат фізико-математичних наук Registration Date 04-01-2023 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2  The aim of the work was to analyze the qualitative behavior of the solutions of the initial and initial-boundary value problems for the new nonstandard as well as classical nonlinear integrable PDEs. Consideration of these problems allowed, first, to substantially develop the existing methods for dealing with such problems and, second, to obtain new important results in the modern theory of integrable systems, which are interesting for mathematicians, physicists and engineers. Within the project we investigated, for the first time, the asymptotic stage of modulation instability for nonlocal integrable NLS equation. Moreover, we discussed the qualitative difference between the obtained results and that known for the classical (local) NLS equation. Also we developed the Deift-Zhou method for studying the long-time asymptotics of the Cauchy problem for the modified Camassa-Holm equation with nonzero boundary conditions. Finally, we investigated the asymptotic behavior of the solution of the initial-boundary value problem for the system of the Maxwell-Bloch equations with spectral broadening and periodic initial signal. Product Description popup.authors popup.nrat_date 2023-01-04 Close