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Yayın Analytical and numerical aspects of the dissipative nonlinear Schrödinger equation(Işık University Press, 2016-02-15) Bayındır, CihanIn this paper various analytical and numerical aspects of the dissipative nonlinear Schrodinger equation (d-NLS equation) are discussed. Decaying solitary wave type solutions derived by Demiray is reviewed and a new approximate solitary wave type solution of the d-NLS equation is introduced in order to make comparisons. Also a split-step Fourier scheme is proposed for numerical solution of the d-NLS equation and the analytical solutions are compared with the numerical results.Yayın Modulational instability of three dimensional waves in a plasma with vortex electron distribution(Işık University Press, 2019-02-10) Demiray, HilmiIn the present work, employing the three dimensional equations of a plasma composed of a cold electron fluid, hot electrons obeying a trapped / vortex-like distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the three dimensional form of the modified nonlinear Schrodinger equation as the evolution equation of the same order of nonlinearity. The modulational instability of the homogeneous harmonic solution is investigated and the criteria for the instability is discussed as a function of the obliqueness angle. The numerical calculations show that the critical value of the wave number of the envelop wave increases with the wave number k of the carrier wave and the obliqueness angle gamma.
