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Article Citation - WoS: 9Citation - Scopus: 10A nonstandard numerical method for the modified KdV equation(indian Acad Sciences, 2017) Aydin, Ayhan; Koroglu, CananA linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg-de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.Article Citation - WoS: 13Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions(Taylor & Francis Ltd, 2009) Aydin, Ayhan; Karasoezen, BuelentSystems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton solutions.Article A New Conservative Numerical Method for Strongly Coupled Nonlinear Schrödinger Equations(Springer Heidelberg, 2025) Ors, Ridvan Fatih; Koroglu, Canan; Aydin, AyhanIn this paper, a numerical method based on the conservative finite difference scheme is constructed to numerically solve the strongly coupled nonlinear Schr & ouml;dinger (SCNLS) equation. Conservative properties such as energy and mass of the SCNLS equation have been proven. In particular a fourth-order central difference scheme is used to discretize the the spatial derivative and a second-order Crank-Nicolson type discretization is used to discretize the temporal derivative. It has been shown that the proposed scheme preserves the discrete mass and energy. The existence of discrete solution is also investigated. Several numerical results are given to demonstrate the preservation properties of the new method. Also, the effect of the linear coupling parameters on the evolution of solitary waves is investigated.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.
