Optical solitons for the fractional $$(3+1)$$ ( 3 + 1 ) -dimensional NLSE with power law nonlinearities by using confo
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ORIGINAL PAPER
Optical solitons for the fractional ð3 þ 1Þ-dimensional NLSE with power law nonlinearities by using conformable derivatives Z Korpinar1, M Inc2,3*
, B Almohsen4 and M Bayram5
1
Department of Administration, Faculty of Economic and Administrative Sciences, Mus Alparslan University, Mus, Turkey 2
Department of Mathematics, Science Faculty, Fırat University, 23119 Elazig, Turkey
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia 5
Department of Computer Engineering, Biruni University, Istanbul, Turkey Received: 12 March 2019 / Accepted: 10 April 2020
Abstract: In this paper, the process of the extended direct algebraic method (EDAM) is used to obtain the optical solitons in fractional (3 ? 1)-dimensional nonlinear Schrodinger equation through the conformable derivative. Firstly, this fractional equation is changed into the ordinary differential equation by using the wave variables transformation. Then, new several forms of optical solitons are obtained by using EDAM. Keywords: Optical solitons; Nonlinear Schrodinger equation; Conformable derivative; Power law nonlinearities; The extended direct algebraic method
1. Introduction Over the past decade, the field of optical solitons has been substantially advanced and enriched by many valuable studies [1–8]. The nonlinear wave process can be viewed in several scientific fields, such as optical fiber, quantum theory, plasma physics and fluid dynamics [9–12]. Solitons are one pulse forms which are created due to the proportion between nonlinearity and wave stage speed dispersal impacts in the system. The envelope soliton which holds both fast and slow vibrations performs for nonlinearity proportions with the wave group dispersal impacts in the physical systems. The envelope soliton is controlled to a small field adjusted wave package whose dynamics are controlled via the nonlinear Schro¨dinger equation (NSE) [1–12]. The analytical solutions of these NPDEs perform a significant part in the analysis of nonlinear phenomena. Numerous methods were developed to obtain exact solutions of NPDEs in the past decades as the extended threesoliton method [13], homotopy perturbation method [14], Hirota’s bilinear method [15], homogeneous balance
method [16], Ba¨cklund transformations [17] and Jacobi and Weierstrass’s elliptic function method [18], and more [19–21]. On the other hand, there have been considerable interests and significant theoretical developments in fractional calculus used in many fields of fractional differential equations and their applicative field [22–28]. There has been much research for nonlinear fractional partial differential equations (FPDEs) which are a specific form of NPDEs. FPDEs are important for various analyses due to their recurrent appearance and versatility and are potentiality put into operations in nonlinear optics, water wave hypothesis, plasma physics
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