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GÜNHAN, NURSENA

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GÜNHAN

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NURSENA

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    Multi wave, kink, breather, interaction solutions and modulation instability to a conformable third order nonlinear schrodinger equation
    (Springer, 2023-04-01) Ay, Nursena Günhan; GÜNHAN, NURSENA; Yaşar, Emrullah; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-1919-2431; 0000-0003-4732-5753; HNT-0160-2023; HOC-4413-2023
    The purpose of this work is the examine the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton solutions for a third-order fractional nonlinear Schrodinger equation (3-FNLS). This model which is vital in fiber optics, explains the propagation of light in optical fibers when ultra-short pulses are produced. We define the model in terms of the conformable time fractional derivative operator so that the model could give a better description of the physical aspect. By picking the activation function in Hirota bilinear form, as the hyperbolic, trigonometric and exponential function along with suitable dispose of parameters, we acquire the three-waves, double exponential, homoclinic breather, and periodic cross kink-soliton auspiciously. Additionally, we have elucidated some three-dimensional and contour portraits to foresee the wave dynamics. These acquired new solutions that do not exist in the literature include some free constants and thereby can be significant to describe variety in qualitative aspects of wave phenomena. At last, we also check the stability of the governing model. By executing the modulation instability analysis, we scrutinize the stability analysis of the yielded exact solutions and the movement role of the waves.
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    Novel dispersive soliton solutions to a fractional nonlinear schrodinger equation related with ultrashort pulses
    (Indian Acad Sciences, 2023-07-12) Ay, Nursena Günhan; GÜNHAN, NURSENA; Yaşar, Emrullah; YAŞAR, EMRULLAH; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-1919-2431; 0000-0003-4732-5753; HNT-0160-2023
    In this study, the third-order fractional nonlinear Schrodinger equation (3-FNLS), which is crucial in fibre optics, is discussed. The equation models propagation of light in optical fibres when ultrashort pulses are generated. In order to explain the physical phenomena, beta, conformable and M-truncated fractional derivative operators are considered. Exact solutions were sought using the extended modified auxiliary equation mapping method (EMAEM). Three-dimensional (3D) and two-dimensional (2D) graphics were designed for each fractional derivative operator of several solutions corresponding to various fractional order values. These graphics were used to study the behaviour of the solutions for conformable, beta and M-truncated fractional derivative operators and to make significant comparisons.