[Turkmath:4278] MSGSU Matematik Genel Semineri-Halis Yılmaz-26 Aralık Perşembe; 16:00

[FATMA ALTUNBULAK AKSU]

Sayın liste üyeleri,

*Herkese Merhaba,*



*MSGSU Matematik Bölümü Genel Seminerinde bu haftaki konuşmacımız Halis
Yılmaz. Seminer ile ilgili tüm detaylar aşağıda yer almaktadır. *



Halis Yılmaz, Dicle Üniversitesi



Başlık:

Darboux Transformations for Integrable Systems



Özet:

 In 1882, the French mathematician Jean Gaston Darboux introduced a method
to solve the Sturm-Louville equation, which is called Darboux
Transformation afterwards.
Darboux transformation is a simultaneous mapping between solutions and
coefficients of a pair of equations of the same form. It may be formulated
as a covariance principle for the corresponding operators, i.e. the order
and form of the operators are saved after the transformation. Almost a
century later, in 1979,  Matveev  realised that the method given by Darboux
for the spectral problem of second order ordinary differential equations
can be extended to some important soliton equations. Darboux
transformations are an important tool for studying the solutions of
integrable systems. They provide
a universal algorithmic procedure to derive explicit exact solutions of
integrable systems. The goal of this talk is to explain the basic ideas of
Darboux transformations for integrable systems.

References

[1] G. Darboux, Comptes Rendus de l'Acadmie des Sciences *94 *(1882)
1456--1459.

[2] V.B. Matveev, Darboux transformation and explicit solutions of the
Kadomtcev-Petviaschvily equation, depending on functional parameters. Lett.
Math. Phys. *3 *(1979) 213--216.

[3] V.B. Matveev and M.A. Salle, Darboux transformations and solitons
(Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin, 1991).

 [4] C.R. Gilson and J.J.C. Nimmo, On a direct approach to quasideterminant
solutions of a noncommutative KP equation, J. Phys. A: Math. Theor. *40 *(14)
(2007) 3839--3850.

 [5] H. Yilmaz, Exact solutions of the Gerdjikov-Ivanov equation using
Darboux transformations, Journal of Nonlinear Mathematical Physics *22 *(1),
32--46 (2015).

Tarih: 26 Aralık Perşembe 2019, 16:00

Yer:  Matematik Bölümü Seminer Odası



*Seminerde görüşmek dileğiyle,*



*Fatma Altunbulak Aksu*

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