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Yayın Freezing optical rogue waves by Zeno dynamics(Elsevier Science BV, 2018-04-15) Bayındır, Cihan; Özaydın, FatihWe investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation domain. Our results can find potential applications in optics including nonlinear phenomena.Yayın A split-step Fourier scheme for the dissipative Kundu-Eckhaus equation and its rogue wave dynamics(Işık University Press, 2021-01) Bayındır, Cihan; Yurtbak, HazalWe investigate the rogue wave dynamics of the dissipative Kundu-Eckhaus equation. With this motivation, we propose a split-step Fourier scheme for its numerical solution. After testing the accuracy and stability of the scheme using an analytical solution as a benchmark problem, we analyze the chaotic wave fields generated by the modulation instability within the frame of the dissipative Kundu-Eckhaus equation. We discuss the effects of various parameters on rogue wave formation probability and we also discuss the role of dissipation on occurrences of such waves.
