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On the Number of Bound States of Semirelativistic Hamiltonian With Dirac Delta Potentials in One Dimension
(National Research Council of Canada, 2018) Erman, Fatih; Erman, Fatih; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
We study the bound state problem for semirelativistic N attractive Dirac delta-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.
Citation - WoS: 8
Citation - Scopus: 8
Some Exact and Explicit Solutions To a Two-Component, Discrete, Nonlinear Schrödinger Model
(National Research Council of Canada, 2011) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
Natural processes and phenomena often display discrete structure. The discrete nonlinear Schrödinger equations are used in both physics and biology to model periodic optical structures and energy transfer in proteins. In this study, we present a new application of the (G'/G)-expansion method to special, coupled, discrete, nonlinear Schrödinger-type equations. This application is shown to be an effective tool for constructing solitary and periodic wave profiles with arbitrary parameters. In addition, we provide rational solutions that have not been explicitly computed before.

Mathematics / Matematik