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UÇAR, MEHMET FATİH

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Dr. Öğr. Üyesi

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UÇAR

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MEHMET FATİH

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    A Study on Harmonic Functions
    (Proceedings of the Bulgarian Academy of Sciences, 2024) UÇAR, MEHMET FATİH; Uçar, Hatice Esra Özkan
    The class of functions that have bounded boundary rotation and bounded radius rotation are the generalization of the convex and the starlike functions, respectively. The concept of such functions was introduced by LOWNER [1]. But he did not use the present terminology. It was PAATERO [2,3] who systematically developed their properties and made an exhaustive study of the class of functions that have bounded boundary rotation. We will examine in this paper, the subclass of S-H H that is related to the class of functions that have bounded radius rotation.
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    Optical Soliton Solution of the Perturbed Fokas-Lenells Equation Having the Cubic-Quintic-Septic Law of Self-Phase Modulation in the Presence of Chromatic and Spatiotemporal Dispersions
    (Springer Science and Business Media Deutschland GmbH, 2024) UÇAR, MEHMET FATİH; Özışık, Müslüm; Seçer, Aydın; Bayram, Mustafa
    This study presents the optical soliton solutions of the Fokas-Lenells equation, which is a significant model for nonlinear optics. The new Kudryashov method is used to obtain the optical solutions in the form of the Fokas-Lenells equation, including the perturbation term and cubic-quintic-septic law nonlinearities. By implementing the method effectively, bright and singular soliton solutions are gained, and graphical presentations were created to analyze the effects of problem parameters on the bright soliton form. The investigated problem parameters include septic law nonlinearity, group velocity dispersion, and spatiotemporal dispersion terms.