Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 12Citation - Scopus: 13On the Exact Solutions of Nonlinear Long-Short Wave Resonance Equations(Editura Acad Romane, 2015) Jafari, H.; Baleanu, Dumitru; Soltani, R.; Khalique, C. M.; Baleanu, D.; MatematikThe long-short wave resonance model arises when the phase velocity of a long wave matches the group velocity of a short wave. In this paper, the first integral method is used to construct exact solutions of the nonlinear long-short wave resonance equations. One-soliton solutions are also obtained using the travelling wave hypothesis.Article Citation - WoS: 19The First Integral Method for The (3+1)-Dimensional Modified Korteweg-De Vries-Zakharov and Hirota Equations(Editura Acad Romane, 2015) Baleanu, D.; Baleanu, Dumitru; Killic, B.; Ugurlu, Y.; Inc, M.; MatematikThe first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations.Article Citation - WoS: 27Citation - Scopus: 18The First Integral Method for Wu-Zhang Nonlinear System With Time-Dependent Coefficients(Editura Acad Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; MatematikThe first integral method is used to construct traveling wave solutions of Wu-Zhang nonlinear dynamical system with time-dependent coefficients. We obtained different types of exact solutions by using two types of variable transformations. The method is an effective tool to construct the different types.of exact solutions of nonlinear partial differential equations having real world applications.Article Citation - Scopus: 38Soliton Solutions of a Nonlinear Fractional Sasa-Satsuma Equation in Monomode Optical Fibers(Natural Sciences Publishing, 2020) Osman, M.S.; Zubair, A.; Raza, N.; Arqub, O.A.; Ma, W.-X.; Baleanu, D.This article is devoted to retrieving soliton solutions of a nonlinear Sasa-Satsuma equation governing the propagation of short light pulses in the monomode optical fibers using the effect of conformable fractional transformation. The Integrability is carried out by incorporating two versatile integration gadgets namely the first integral method and the generalized projective Riccati equation method. The resulting solutions include bright, dark, singular, periodic as well as rational solitons along with their existence criteria. Furthermore, the fractional behavior of the solutions is investigated comprehensively using graphs. © 2020 NSP Natural Sciences Publishing Cor.Article Citation - WoS: 10Exact Solutions of Two Nonlinear Partial Differential Equations by Using the First Integral Method(Springer, 2013) Soltani, Rahmat; Khalique, Chaudry Masood; Baleanu, Dumitru; Jafari, HosseinIn recent years, many approaches have been utilized for finding the exact solutions of nonlinear partial differential equations. One such method is known as the first integral method and was proposed by Feng. In this paper, we utilize this method and obtain exact solutions of two nonlinear partial differential equations, namely double sine-Gordon and Burgers equations. It is found that the method by Feng is a very efficient method which can be used to obtain exact solutions of a large number of nonlinear partial differential equations.Article Citation - WoS: 18Citation - Scopus: 23First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models(Mdpi, 2019) Riaz, Sidra; Alimgeer, Khurram Saleem; Atif, M.; Hanif, Atif; Baleanu, Dumitru; Javeed, ShumailaIn this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.Article Citation - WoS: 185Citation - Scopus: 199New Exact Solutions of Burgers' Type Equations With Conformable Derivative(Taylor & Francis Ltd, 2017) Baleanu, Dumitru; Kurt, Ali; Tasbozan, Orkun; Cenesiz, YucelIn this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers' equation, modified Burgers' equation, and Burgers-Korteweg-de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs.Article The first integral method for the (3+1)-dimensional modified korteweg-de vries-zakharov-kuznetsov and hirota equations(Editura Academiei Romane, 2015) Baleanu, Dumitru; Kılıç, B.; Uğurlu, Y.; İnç, MustafaThe first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations