<div dir="ltr"><br clear="all"><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><br></div><div dir="ltr"><br></div></div></div></div></div></div><div class="gmail_quote"> <div class="m_8919134170454713549F0XO1GC-nb-gb"><div class="m_8919134170454713549F0XO1GC-H-d"><input style="opacity:0;height:1px;width:1px;overflow:hidden" type="text"><span></span></div></div> <div class="m_8919134170454713549F0XO1GC-ed-a"> <div class="m_8919134170454713549F0XO1GC-nb-P"><input style="opacity:0;height:1px;width:1px;overflow:hidden" type="text"><div><div style="overflow:auto"><div style="max-height:10000px"><div dir="ltr"><div><div style="overflow:auto"><div style="max-height:10000px"><div dir="ltr"><p style="text-align:center;clear:both"><a href="https://lh3.googleusercontent.com/-ZPFNPh16sR0/Wt39FrXUP-I/AAAAAAAAAaw/3wQunGe20lUopmV_ggfPaDwE9cVAgVzxgCLcBGAs/s1600/image001.jpg" style="margin-left:1em;margin-right:1em" target="_blank"><img src="https://lh3.googleusercontent.com/-ZPFNPh16sR0/Wt39FrXUP-I/AAAAAAAAAaw/3wQunGe20lUopmV_ggfPaDwE9cVAgVzxgCLcBGAs/s1600/image001.jpg" border="0"></a></p><br>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">DATE:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Friday, February 15, 2019</span></b></p>
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<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">TITLE:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <br></span></p><p class="MsoNormal" style="text-align:center" align="center"><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <br></span></p><p class="MsoNormal" style="text-align:center" align="center"><font size="6"><span style="font-family:verdana,sans-serif"></span></font></p><p class="MsoNormal" style="text-align:center" align="center"><font size="6"><span style="font-family:verdana,sans-serif"><b><span style="background:white none repeat scroll 0% 0%"></span></b></span></font></p><div style="text-align:center"><span style="font-family:verdana,sans-serif"><font size="6"><b><span></span></b></font></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span></span></b></font></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span></span></b></font></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span></span></b></font></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span>Solutions to Nonlinear Differential Systems via the Hirota Bilinear Method</span></b></font><br></span><span style="font-family:verdana,sans-serif"><font size="6"><b><span style="font-size:11pt"></span></b> </font></span></div><p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black"> </span></p>
<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black"><br></span></p><p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">TIME:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> </span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">3<span style="color:black">:30PM</span></span></b></p>
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<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">LOCATION:</span><span style="font-size:10.0pt;font-family:"Verdana",sans-serif;color:black"> <b> </b></span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">GMCS 314</span></b></p>
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<p class="MsoNormal" style="text-align:center" align="center"><span style="font-family:"Verdana",sans-serif;color:black">SPEAKER/BIO:</span><span style="font-size:13.5pt;font-family:"Verdana",sans-serif;color:black"> </span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"><br></span></b></p><p class="MsoNormal" style="text-align:center" align="center"><br><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b></p><p class="MsoNormal" style="text-align:center" align="center"><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif">Dr. Luis Cisneros-Ake, Fulbright Visiting Scholar, SDSU, and Professor of Mathematics, National Polytechnic Institute, Mexico<br></span></b><font size="4"><span style="font-family:verdana,sans-serif"><b><span><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"><span style="color:black"></span></span></b></span><span></span></b></span></font></p><p class="MsoNormal" style="text-align:center" align="center"><b><span style="font-size:18.0pt;font-family:"Verdana",sans-serif"></span></b></p>
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<p class="MsoNormal"><span style="font-family:"Verdana",sans-serif;color:black"><br></span></p><p class="MsoNormal"><span style="font-family:"Verdana",sans-serif;color:black">ABSTRACT:</span></p><font size="4"><span style="font-family:verdana,sans-serif">The dynamics of weakly nonlinear oscillators is presented as a prototype
of nonlinear evolution systems where the propagation of coherent
localized solutions take place. We show that the continuous medium,
corresponding to the long wave limit, corresponds to the classical
Korteweg-de Vries (KdV) equation. We then explain, in some detail, the
basics of the Direct Method due to Hirota and how it can be applied in
solving the KdV equation. We finish considering, if time permits, other
nonlinear systems of interest where Hirota's method can be used.</span></font></div><font size="4"><span style="font-family:verdana,sans-serif"><br></span></font><h2><span style="font-size:11.0pt;font-family:"Verdana",sans-serif;color:black;font-weight:normal">HOST: </span>Ricardo Carretero</h2></div></div></div></div></div></div></div></div></div><table class="m_8919134170454713549F0XO1GC-nb-O" cellspacing="0" cellpadding="0"><tbody><tr><td class="m_8919134170454713549F0XO1GC-nb-R" valign="top" align="left"><span class="m_8919134170454713549_username"><span class="m_8919134170454713549F0XO1GC-D-a" style="color:rgb(34,34,34)"></span></span> <span></span> </td> <td valign="top" align="right"> <div class="m_8919134170454713549F0XO1GC-nb-e"><div class="m_8919134170454713549F0XO1GC-n-a m_8919134170454713549jfk-button-standard m_8919134170454713549F0XO1GC-n-f m_8919134170454713549F0XO1GC-nb-i m_8919134170454713549F0XO1GC-nb-A"><img src="cid:autoGeneratedInlineImage1" class="m_8919134170454713549gwt-Image m_8919134170454713549F0XO1GC-n-d" width="21" height="21"><input style="opacity:0;height:1px;width:1px;overflow:hidden" type="text"><span class="m_8919134170454713549F0XO1GC-n-e"></span></div><span class="m_8919134170454713549F0XO1GC-nb-i m_8919134170454713549F0XO1GC-nb-f"><div class="m_8919134170454713549F0XO1GC-n-a m_8919134170454713549jfk-button-standard m_8919134170454713549F0XO1GC-k-c m_8919134170454713549F0XO1GC-nb-k m_8919134170454713549F0XO1GC-n-i m_8919134170454713549F0XO1GC-n-h" id="m_8919134170454713549b_action_n1Bt84waIAAJ"><input style="opacity:0;height:1px;width:1px;overflow:hidden" type="text"><span class="m_8919134170454713549F0XO1GC-n-e"><span></span></span><span class="m_8919134170454713549F0XO1GC-k-a"><span class="m_8919134170454713549F0XO1GC-k-b"></span></span></div></span></div> <div class="m_8919134170454713549F0XO1GC-nb-R m_8919134170454713549F0XO1GC-nb-T"> <span class="m_8919134170454713549F0XO1GC-nb-Q m_8919134170454713549F0XO1GC-b-Db" title="Monday, February 4, 2019 at 8:30:04 AM UTC-8">Feb 4</span> </div> </td> </tr> </tbody></table>
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