DSpace@Isik UniversityDSpace dijital arşiv sistemi toplar, depolar, dizinler, korur ve dijital araştırma materyallerini dağıtmaya aracılık eder.http://acikerisim.isikun.edu.tr:8080/xmlui2018-07-16T10:54:43Z2018-07-16T10:54:43ZExact Solution Of Perturbed Kdv Equation With Variable Dissipation CoefficientDemiray, Hilmihttp://hdl.handle.net/11729/13162018-06-22T13:14:04Z2017-01-01T00:00:00ZExact Solution Of Perturbed Kdv Equation With Variable Dissipation Coefficient
Demiray, Hilmi
In the present work we study the integrability condition for a variable coefficient Korteweg-deVries(KdV) equation. For that purpose, we first introduce some proper transformations for dependent and independent variables in such a way that the variable coefficient KdV equation reduces to the perturbed KdV equation with variable dissipation coefficient. Then, we apply the homogeneous balance (HB) method to this perturbed KdV equation to examine the integrability condition for this equation. The analysis reveals that if the dissipation coefficient function has a special structure the variable coefficient KdV equation is integrable. The progressive wave solution of evolution equation shows that the solution is unbounded and the wave amplitude decreases with time, which is to be expected from physical considerations.
2017-01-01T00:00:00ZRogue wavefunctions due to noisy quantum tunneling potentialsBayındır, Cihanhttp://hdl.handle.net/11729/13152018-06-23T00:00:09Z2017-01-01T00:00:00ZRogue wavefunctions due to noisy quantum tunneling potentials
Bayındır, Cihan
In this paper, we study the effects of white-noised potentials on nonlinear quantum tunneling. We use a split-step scheme to numerically solve the nonlinear Schrodinger equation (NLSE) with a tunneling potential. We consider three different types of potentials, namely; the single rectangular barrier, double rectangular barrier, and triangular barrier. For all these three cases, we show that white-noise given to potentials do not trigger modulation instability for tunneling of the sech type soliton solutions of the NLSE. However, white-noised potentials trigger modulation instability for tunneling of the sinusoidal wavefunctions; thus, such a wavefield turns into a chaotic one with many apparent peaks. We argue that peaks of such a field may be in the form of rational rogue wave solutions of the NLSE. Our results can be used to examine the effects of noise on quantum tunneling. Since a rogue wavefunction means a higher probability of the tunneling particle to be at a given (x,t) coordinate, our results may also be used for developing the quantum science and technology with many possible applications including but are not limited to increasing the resolution and efficiency of scanning tunneling microscopes, enhancing proton tunneling for DNA mutation and enhancing superconducting properties of junctions.
2017-01-01T00:00:00ZOn the fractional Fourier and continuous fractional wave packet transforms of almost periodic functionsUzun Ünalmış, Banuhttp://hdl.handle.net/11729/13142018-06-22T00:00:19Z2017-06-02T00:00:00ZOn the fractional Fourier and continuous fractional wave packet transforms of almost periodic functions
Uzun Ünalmış, Banu
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
2017-06-02T00:00:00ZOn approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equationsAydogan, Seher MelikeBaleanu, DumitruMousalou, AsefRezapour, Shahramhttp://hdl.handle.net/11729/13132018-06-22T00:00:18Z2017-08-03T00:00:00ZOn approximate solutions for two higher-order Caputo-Fabrizio fractional integro-differential equations
Aydogan, Seher Melike; Baleanu, Dumitru; Mousalou, Asef; Rezapour, Shahram
We investigate the existence of solutions for two high-order fractional differential equations including the Caputo-Fabrizio derivative. In this way, we introduce some new tools for obtaining solutions for the high-order equations. Also, we discuss two illustrative examples to confirm the reported results. In this way one gets the possibility of utilizing some continuous or discontinuous mappings as coefficients in the fractional differential equations of higher order.
2017-08-03T00:00:00Z