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<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style="mso-bidi-font-weight:normal"><span style="font-size:13pt;font-family:"Times New Roman",serif">Three conservative schemes for the 3-coupled nonlinear
Schrödinger equation</span></b></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal" align="center"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif">Ayhan Aydın</span></b></p>
<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:center;line-height:normal" align="center"><b style="mso-bidi-font-weight:normal"><span style="font-size:14pt;font-family:"Times New Roman",serif">Atılım University, Türkiye</span></b></p>
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<p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;line-height:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif">Özet : The
N-coupled nonlinear Schrödinger (N-CNLS) equation arises as the governing model
equation in several branches of physics including, for example, optics, fluid
dynamics, quantum mechanics and biophysics. In the last decades, there has been
an increased interest in numerical preservation of one or more
physical/geometric properties of the mechanical system under consideration.
There has been a lot of works on the numerical solution of the single NLS and
the coupled NLS (2-CNLS) equation such as symplectic and multisymplectic
schemes, the Hopscotch method, Galerkin finite element method, a fourth-order
explicit Runge-Kutta method, and so on. Recently, the main attention for the
2-CNLS equation is the mass and the energy preserving schemes. Although, there
are many numerical studies on the NLS and the 2-CNLS, numerical studies for
N-CNLS equation with N>=3 are rare. In this study, 3-CNLS is considered. In
particular, three conservative schemes are proposed; namely, (i) a scheme that
conserves the energy,(ii) a linearly implicit three-level scheme that conserves
the mass, and (iii) a two-level scheme that conserves both the mass and the
energy of the 3-CNLS equation. Many numerical results are carried out to test
the efficiency and reliability of the proposed schemes. The numerical results show
that the proposed schemes have excellent performance in simulating the plane
wave, periodic, single and colliding soliton solutions of the 3-CNLS equation
during long-time integration. This work is supported by The Scientific and
Technological Research Council of Turkey (TUBITAK) with the project number
114F020. It is a joint work with Sevim Ertuğ (M.Sc. Student, Math.Dept, Atilim
University) </span></p>
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<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style="mso-bidi-font-weight:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif">23.12.2015</span></b></p>
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<p class="MsoNormal" style="margin-bottom:0.0001pt;line-height:normal"><b style="mso-bidi-font-weight:normal"><span style="font-size:12pt;font-family:"Times New Roman",serif">İngilizce</span></b></p>
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<div><div class="gmail_signature"><div dir="ltr"> <br><br> Mesut Sahin<div> Associate Professor<br> Department of Mathematics<br> Hacettepe University<br> TR 06800 Beytepe </div><div> ANKARA - TURKEY<br> <a href="http://yunus.hacettepe.edu.tr/~mesut.sahin" target="_blank">http://yunus.hacettepe.edu.tr/~mesut.sahin</a></div></div></div></div>
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