[Turkmath:898] Hacettepe Üniversitesi Bölüm Seminerleri, Ayhan Aydın (Atılım), 23 Aralık 2015

[Mesut Şahin]

*Three conservative schemes for the 3-coupled nonlinear Schrödinger
equation*

*Ayhan Aydın*

*Atılım University, Türkiye*



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)



*Tarih*

*:*

*23.12.2015*



*Saat*

*:*

*15:00*



*Yer*

*:*

*Yaşar Ataman Salonu, Matematik Bölümü*



*Dil*

*:*

*İngilizce*




  Mesut Sahin
  Associate Professor
  Department of Mathematics
  Hacettepe University
  TR 06800 Beytepe
  ANKARA - TURKEY
 http://yunus.hacettepe.edu.tr/~mesut.sahin
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