3 research outputs found

    A New Six Point Finite Difference Scheme for Nonlinear Waves Interaction Model

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    In the paper, the coupled 1D Klein-Gordon-Zakharov system (KGZ-equations in short) is considered as the model equation for wave-wave interaction in ionic media. A finite difference scheme is derived for the model equations. A new six point scheme, which is equivalent to the multi-symplectic integrator, is derived. The numerical simulation is also presented for the model equations. Keywords: Coupled 1D Klein-Gordon-Zakharov system; Energy conservation; Six-point schem

    İkili drinfel’d-sokolov-wilson denklemlerinin modifiyesi ve yaklaşık çözümleri için optimal perturbasyon iterasyon metodu

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    We try to find the semi-analytical approximate solutions for the system of partial differential equations by using a newly developed scheme. The optimal perturbation iteration method is introduced and then applied to a newly modified coupled Drinfel’d-Sokolov-Wilson equation. Classical perturbation theory and optimization techniques are combined to construct this method. We will deeply analyze an example to prove the power of the proposed method, namely the optimal perturbation iteration method. With the theorem and applications, we see that the present study shows that the new method converges fast to the accurate analytical solutions of the considered equations at even the first two-three iterations.Bu araştırma makalesinde, kısmi diferansiyel denklemler sistemi için yeni geliştirilen bir metot yardımıyla yarı analitik çözümler bulmaya çalışıyoruz. Optimal perturbasyon iterasyon yöntemini tanıtıyor ve sonra yeniden modifiye edilen ikili Drinfel’d-Sokolov-Wilson denklemine uyguluyoruz. Klasik perturbasyon teorisi ve optimizasyon teknikleri birleştirilerek bu yöntemi inşa ediyoruz. Optimal perturbasyon iterasyon olarak önerilen metodun gücünü göstermek için özel bir örneği derinlemesine irdeliyoruz. Teorem ve uygulamalar önerilen tekniğin ele alınan denklemler için iterasyonun daha ilk basamaklarında tam çözüme hızlı bir şekilde yaklaştığını göstermektedir

    On consistent systems of difference equations

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    We consider overdetermined systems of difference equations for a single function u which are consistent, and propose a general framework for their analysis. The integrability of such systems is defined as the existence of higher order symmetries in both lattice directions and various examples are presented. Two hierarchies of consistent systems are constructed, the first one using lattice paths and the second one as a deformation of the former. These hierarchies are integrable and their symmetries are related via Miura transformations to the Bogoyavlensky and the discrete Sawada-Kotera lattices, respectively
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