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Article Citation - WoS: 12Citation - Scopus: 12Boundary Value Problems for Nonlinear Impulsive Hamiltonian Systems(Elsevier Science Bv, 2014) Guseinov, Gusein Sh.We study two point boundary value problems for nonlinear impulsive Hamiltonian systems. Spectral analysis of the corresponding linear impulsive Hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem. Two examples are given in which the main condition is made explicit. (C) 2013 Elsevier B.V. All rights reserved.Article New Conservative Schemes for Zakharov Equation(Association of Mathematicians (MATDER), 2023) Aydin,A.; Sabawe,B.A.K.New first-order and second-order energy preserving schemes are proposed for the Zakharov system. The methods are fully implicit and semi-explicit. It has been found that the first order method is also massconserving. Concrete schemes have been applied to simulate the soliton evolution of the Zakharov system. Numerical results show that the proposed methods capture the remarkable features of the Zakharov equation. We have obtained that the semi-explicit methods are more efficient than the fully implicit methods. Numerical results also demonstrate that the new energy-preserving schemes accurately simulate the soliton evolution of the Zakharov system. © MatDer.Article Citation - WoS: 79Citation - Scopus: 86Lyapunov inequalities for discrete linear Hamiltonian systems(Pergamon-elsevier Science Ltd, 2003) Guseinov, GS; Kaymakçalan, BIn this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end-points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems. (C) 2003 Elsevier Science Ltd. All rights reserved.
