Browsing by Author "Adem, Abdullahi Rashid"
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Item Complexiton solutions and soliton solutions: (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation(Indian Academy Sciences, 2018-07-23) Adem, Abdullahi Rashid; Yıldırım, Yakup; Yasar, Emrullah; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300In this work, we derive the complexiton solutions for Date-Jimbo-Kashiwara-Miwa (DJKM) equation using the extended transformed rational function algorithm that relies on the Hirota bilinear form of the considered equation. Additional solutions such as complex-valued solutions also fall out of this integration scheme. Multisoliton-type solutions, in other words one-soliton, two-soliton and three-soliton solutions, which comprise both wave frequencies and generic phase shifts are presented through the medium of the multiple exp-function methodology which falls out as a result of generalisation of Hirota's perturbation technique.Publication Extended transformed rational function method to nonlinear evolution equations(Walter, 2019-10-01) Yaşar, Emrullah; Yıldırım, Yakup; Adem, Abdullahi Rashid; YAŞAR, EMRULLAH; Yıldırım, Yakup; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4732-5753; 0000-0003-4443-3337; AAG-9947-2021; HTO-9875-2023In this work, we study complexiton solutions to a (2+1)-dimensional (SK) equation and a (3+1)dimensional nonlinear evolution equation. The complexiton solutions are combinations of trigonometric function waves and exponential function waves. For this goal, the extended transformed rational function method is carried out which is based on the Hirota bilinear forms of the considered equations and provides a systematical and convenient tool for constructing the exact solutions of nonlinear evolution equations.Item A multiple exp-function method for the three model equations of shallow water waves(Springer, 2017-05-25) Adem, Abdullahi Rashid; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300In this study, we consider three model equations of shallow water waves. Shallow water equations model the propagation of strongly nonlinear waves up to breaking and run-up in nearshore zones. We perform multiple exp-function method which is known as a generalization of Hirota's perturbation scheme. We yield one-, two-, and three-wave solutions. The obtained solutions can be used as benchmarks for numerical solutions of the underlying equations.Item Perturbed optical solitons with spatio-temporal dispersion in (2+1) -dimensions by extended Kudryashov method(Elsevier, 2018) Adem, Abdullahi Rashid; Yaşar, Emrullah; Yıldırım, Yakup; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; 0000-0003-4443-3337; AAG-9947-2021; HTO-9875-2023; 23471031300; 56988856400This paper derives optical soliton solutions to perturbed nonlinear Schrodinger's equation with spatio-temporal dispersion in (2 + 1)-dimensions by the extended Kudryashov method which takes full advantages of the Bernoulli and Riccati equations to construct optical soliton solutions. There are four types of nonlinear fibers studied in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law and triple-power law nonlinearity. With performing this algorithm, dark soliton, singular soliton and rational soliton are deduced. These solitons are important in optics. Besides, singular periodic solutions are revealed as a consequences of this approach and these are also listed. (C) 2017 Elsevier GmbH. All rights reserved.Publication Soliton solutions to the non-local boussinesq equation by multiple exp-function scheme and extended kudryashov's approach(Indian Acad Sciences, 2019-02-01) Adem, Abdullahi Rashid; Yıldırım, Yakup; Yaşar, Emrullah; Yıldırım, Yakup; YAŞAR, EMRULLAH; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0003-4443-3337; 0000-0003-4732-5753; AAG-9947-2021; HTO-9875-2023In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark-singular soliton-type solutions of nlBq by the extended Kudryashov's algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.Publication The logarithmic (1+1)-dimensional KdV-like and (2+1)-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions(Gmbh, 2019-12-01) Giresunlu, İlker Burak; Yaşar, Emrullah; Adem, Abdullahi Rashid; YAŞAR, EMRULLAH; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAG-9947-2021We investigate the logarithmic (1 + 1) dimensional KdV-like and (2 + 1) dimensional KP-like equations which model many physical processes in the field of soliton theory. In this paper, first, we get the classical Lie point symmetries using the invariance theory. Secondly, we obtain conservation laws of the underlying equations by incorporating the method of multiplier and non-local conservation method. A relationship between the obtained symmetries and conservation laws are shown. Then using the generalized double reduction theory for the associated symmetries, reductions are constructed. Finally traveling wave solutions are computed with the aid of the simplest equation method for the logarithmic (2 + 1)-dimensional KP-like equation.