<div dir="ltr"><div>Sayın liste üyeleri,</div><div><br></div><div>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif"">Herkese
Merhaba,</span></i><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif"">MSGSU
Matematik Bölümü Genel Seminerinde bu haftaki konuşmacımız Halis Yılmaz.
Seminer ile ilgili tüm detaylar aşağıda yer almaktadır. </span></i><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Halis Yılmaz,
Dicle Üniversitesi<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Başlık:<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Darboux
Transformations for Integrable Systems<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Özet:<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif""> </span><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif"">In 1882, the French mathematician Jean Gaston
Darboux introduced a method to solve the Sturm-Louville equation, which is
called Darboux Transformation afterwards. <br>
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<br>
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.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif"">References<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif"">[1] G. Darboux, Comptes Rendus de l'Acadmie des Sciences <b>94 </b>(1882) 1456--1459.</p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif"">
[2] V.B. Matveev, Darboux transformation and explicit solutions of the
Kadomtcev-Petviaschvily equation, depending on functional parameters. Lett.
Math. Phys. <b>3 </b>(1979) 213--216.</p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif"">
[3] V.B. Matveev and M.A. Salle, Darboux transformations and solitons (Springer
Series in Nonlinear Dynamics, Springer-Verlag, Berlin, 1991).</p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""> [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. <b>40 </b>(14) (2007) 3839--3850. <br></p><p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""> [5] H. Yilmaz, Exact solutions of the Gerdjikov-Ivanov equation using
Darboux transformations, Journal of Nonlinear Mathematical Physics <b>22 </b>(1), 32--46 (2015).<span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif"">Tarih: 26 Aralık Perşembe 2019, 16:00<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif";color:black">Yer: Matematik Bölümü Seminer Odası</span><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif";color:black"> </span><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif";color:black">Seminerde görüşmek dileğiyle,<span></span></span></i></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif";color:black"><span> </span></span></i></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif";color:black">Fatma Altunbulak Aksu</span></i><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""></span><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span> </span></p>
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