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Article Citation - WoS: 24Citation - Scopus: 24Symplectic and multisymplectic Lobatto methods for the "good" Boussinesq equation(Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.In this paper, we construct second order symplectic and multisymplectic integrators for the "good" Boussineq equation using the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method, which yield an explicit scheme and is equivalent to the classical central difference approximation to the second order spatial derivative. Numerical dispersion properties and the stability of both integrators are investigated. Numerical results for different solitary wave solutions confirm the excellent long time behavior of symplectic and multisymplectic integrators by preservink local and global energy and momentum. (C) 2008 American Institute of Physics.Article Citation - WoS: 16Citation - Scopus: 15Dynamical Systems and Poisson Structures(Amer inst Physics, 2009) Guerses, Metin; Guseinov, Gusein Sh; Zheltukhin, KostyantynWe first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919]Article Citation - WoS: 14Citation - Scopus: 15Activation Energy of Metastable Amorphous Ge2sb2< From Room Temperature To Melt(Amer inst Physics, 2018) Muneer, Sadid; Scoggin, Jake; Dirisaglik, Faruk; Adnane, Lhacene; Cywar, Adam; Bakan, Gokhan; Gokirmak, AliResistivity of metastable amorphous Ge2Sb2Te5 (GST) measured at device level show an exponential decline with temperature matching with the steady-state thin-film resistivity measured at 858 K (melting temperature). This suggests that the free carrier activation mechanisms form a continuum in a large temperature scale (300 K - 858 K) and the metastable amorphous phase can be treated as a supercooled liquid. The effective activation energy calculated using the resistivity versus temperature data follow a parabolic behavior, with a room temperature value of 333 meV, peaking to similar to 377 meV at similar to 465 K and reaching zero at similar to 930 K, using a reference activation energy of 111 meV (3k(B)T/2) at melt. Amorphous GST is expected to behave as a p-type semiconductor at T-melt similar to 858 K and transitions from the semiconducting-liquid phase to the metallic-liquid phase at similar to 930 K at equilibrium. The simultaneous Seebeck (S) and resistivity versus temperature measurements of amorphous-fcc mixed-phase GST thin-films show linear S-T trends that meet S = 0 at 0 K, consistent with degenerate semiconductors, and the dS/dT and room temperature activation energy show a linear correlation. The single-crystal fcc is calculated to have dS/dT = 0.153 mu V/K-2 for an activation energy of zero and a Fermi level 0.16 eV below the valance band edge. (C) 2018 Author(s).Article Citation - WoS: 17Citation - Scopus: 16Multisymplectic Box Schemes for the Complex Modified Korteweg-De Vries Equation(Amer inst Physics, 2010) Aydin, A.; Karasozen, B.In this paper, two multisymplectic integrators, an eight-point Preissman box scheme and a narrow box scheme, are considered for numerical integration of the complex modified Korteweg-de Vries equation. Energy and momentum preservation of both schemes and their dispersive properties are investigated. The performance of both methods is demonstrated through numerical tests on several solitary wave solutions. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456068]Article Citation - WoS: 44Citation - Scopus: 46Integrable Equations on Time Scales -: Art. No. 113510(Amer inst Physics, 2005) Gürses, M; Guseinov, GS; Silindir, BIntegrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on K-q). We formulate the Gel'fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over q-numbers (q-difference equations). We formulate the GD formalism also in terms of shift operators for all regular-discrete time scales. We give a method allowing to construct the recursion operators for integrable systems on time scales. Finally, we give a trace formula on time scales and then construct infinitely many conserved quantities (Casimirs) of the integrable systems on time scales. (c) 2005 American Institute of Physics.
