Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 6Citation - Scopus: 6Lump-Type and Bell-Shaped Soliton Solutions of the Time-Dependent Coefficient Kadomtsev-Petviashvili Equation(Frontiers Media Sa, 2020) Li, Yongjin; Qi, Liu; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Aliyu, Aliyu IsaIn this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz. The equation is applied in the modeling of propagation of small-amplitude surface waves in large channels or straits of slowly varying width, depth and non-vanishing vorticity. Applying the Bell's polynomials approach, we successfully acquire the bilinear form of the equation. We firstly find a general form of quadratic function solution of the bilinear form and then expand it as the sums of squares of linear functions satisfying some conditions. Most importantly, we acquire two lump-type and a bell-shaped soliton solutions of the equation. To our knowledge, the lump type solutions of the equation are reported for the first time in this paper. The physical interpretation of the results are discussed and represented graphically.Article Citation - WoS: 88Citation - Scopus: 94Optical Solitons Possessing Beta Derivative of the Chen-Lee Equation in Optical Fibers(Frontiers Media Sa, 2019) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, AbdullahiThis research obtains some new optical soliton solutions with beta derivative for Chen-Lee-Liu equation (CLL) in optical fibers. Three integration schemes which are Ricatti-Bernoulli (RB) sub-ODE, generalized Bernoulli (GB) sub-ODE and generalized tanh (GT) methods are applied to reach such solutions. The constraints conditions for the existence of soliton solutions are reported. The solutions are obtained using newly introduced fractional derivative called beta derivative. Numerical simulations of some of the obtained solutions are illustrated.