Archives and Documentation Center
Digital Archives

Algebro-geometric solutions of the kadomtsev-petviashvili equation

Show simple item record

dc.contributor Graduate Program in Mathematics.
dc.contributor.advisor Gürel, Burak.
dc.contributor.advisor Boysal, Arzu.
dc.contributor.author Çiçek, Fatma.
dc.date.accessioned 2023-03-16T11:21:40Z
dc.date.available 2023-03-16T11:21:40Z
dc.date.issued 2014.
dc.identifier.other MATH 2014 C53
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/15276
dc.description.abstract I. M. Krichever suggested a method to solve nonlinear partial di erential equations in the form of the Zaharov-Shabat Equation [L {u100000} @y;A {u100000} @t] = 0 where L and A are di erential operators including derivatives only with respect to the x variable in 1976 [1]. The method uses so called Baker-Akhiezer functions on Riemann surfaces and provides periodic and conditionally periodic solutions to such nonlinear equations that can be expressed in terms of the so called Riemann -function, a -function de- ned on some n dimensional complex space where the Riemann matrix of the function corresponds to a Riemann surface. In this thesis, we will mainly consider the Kadomtsev-Petviashvili equation (or KP equation) 3 4 uyy = @ @x ut {u100000} 1 4 (6uux + uxxx) which is an example of the Zaharov-Shabat equation. Following the expository paper of B. A. Dubrovin [2], we will present the construction of such solutions to the KP equation given as u(x; y; t) = 2 @2 @x2 log (xU +yV +tW +z0)+c. It was observed that this construction allows one to investigate the su cient conditions on arbitrary vectors U, V , and W that make the above function u(x; y; t) a solution to the KP equation. We explain the answer to this question for Riemann surfaces of small genera, and mention the result for more general Riemann surfaces which are both given in [2].
dc.format.extent 30 cm.
dc.publisher Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2014.
dc.subject.lcsh Nonlinear waves -- Mathematical models.
dc.title Algebro-geometric solutions of the kadomtsev-petviashvili equation
dc.format.pages leaves ;


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search Digital Archive


Browse

My Account