Reality conditions for the KdV equation and exact quasi-periodic solutions in finite phase spaces

Simple item page
dc.contributor.authorBernatska, Juliaen_US
dc.date.accessioned2024-10-23T05:23:19Z
dc.date.available2024-10-23T05:23:19Z
dc.date.issued2024
dc.description.abstractIn the present paper reality conditions for quasi-periodic solutions of the KdV equation are determined completely. As a result, solutions in the form of non-linear waves can be plotted and investigated. The full scope of obtaining finite-gap solutions of the KdV equation is presented. It is proven that the multiply periodic }1, 1-function on the Jacobian variety of a hyperelliptic curve of arbitrary genus serves as the finite-gap solution, the genus coincides with the number of gaps. The subspace of the Jacobian variety where }1, 1, as well as other }-functions, are bounded and real-valued is found in any genus. This result covers every finite phase space of the KdV hierarchy, and can be extended to other completely integrable equations. A method of effective computation of this type of solutions is suggested, and illustrated in genera 2 and 3.en_US
dc.identifier.citationBernatska J. N. Reality conditions for the KdV equation and exact quasi-periodic solutions in finite phase spaces / Julia Bernatska // Journal of Geometry and Physics. - 2024. - Vol. 206. - Art. no. 105322. - 34 p. - https://doi.org/10.48550/arXiv.2312.10859en_US
dc.identifier.issn0393-0440
dc.identifier.urihttps://doi.org/10.48550/arXiv.2312.10859
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/31937
dc.language.isoenen_US
dc.relation.sourceJournal of Geometry and Physicsen_US
dc.statusfirst publisheden_US
dc.subjectKdV equationen_US
dc.subjectquasi-periodic solutionsen_US
dc.subjectfunction on the Jacobianen_US
dc.subjectintegrable equationsen_US
dc.subjectarticleen_US
dc.titleReality conditions for the KdV equation and exact quasi-periodic solutions in finite phase spacesen_US
dc.typeArticleen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Bernatska_Reality_conditions_for_the_KdV_equation_and_exact_quasi-periodic_solutions_in_finite_phase_spaces.pdf
Size:
1.18 MB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Кафедра фізико-математичних наук