Conservative finite difference schemes for the chiral nonlinear Schrödinger equation

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2015

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Boundary Value Problems

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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In this paper, we derive three finite difference schemes for the chiral nonlinear Schrödinger equation (CNLS). The CNLS equation has two kinds of progressive wave solutions: bright and dark soliton. The proposed methods are implicit, unconditionally stable and of second order in space and time directions. The exact solutions and the conserved quantities are used to assess the efficiency of these methods. Numerical simulations of single bright and dark solitons are given. The interactions of two bright solitons are also displayed.

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mathematics

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https://hdl.handle.net/20.500.14411/6397

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