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Article Citation - WoS: 4Citation - Scopus: 5An Unconventional Finite Difference Scheme for Modified Korteweg-De Vries Equation(Hindawi Ltd, 2017) Koroglu, Canan; Aydin, AyhanA numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.Article Citation - WoS: 23Citation - Scopus: 25Multisymplectic Integration of n-coupled Nonlinear Schrodinger Equation With Destabilized Periodic Wave Solutions(Pergamon-elsevier Science Ltd, 2009) Aydin, AyhanN-coupled nonlinear Schrodinger equation (N-CNLS) is shown to be in multisymplectic form. 3-CNLS equation is studied for analytical and numerical purposes. A new six-point scheme which is equivalent to the multisymplectic Preissman scheme is derived for 3-CNLS equation. A new periodic wave solution is obtained and its stability analysis is discussed. 3-CNLS equation is integrated for destabilized periodic solutions both for integrable and non-integrable cases by multisymplectic six-point scheme. Different kinds of evolutions are observed for different parameters and coefficients of the system. Numerical results show that, the multisymplectic six-point scheme has excellent local and global conservation properties in long-time computation. (C) 2008 Elsevier Ltd. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 12Conservative Finite Difference Schemes for the Chiral Nonlinear Schrodinger Equation(Springer international Publishing Ag, 2015) Ismail, Mohammad S.; Al-Basyouni, Khalil S.; Aydin, AyhanIn this paper, we derive three finite difference schemes for the chiral nonlinear Schrodinger 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.
