scispace - formally typeset
Journal ArticleDOI: 10.1080/17455030.2019.1579393

New wave form solutions of nonlinear conformable time-fractional Zoomeron equation in (2 + 1)-dimensions

04 Mar 2021-Waves in Random and Complex Media (Taylor & Francis)-Vol. 31, Iss: 2, pp 228-238
Abstract: Under investigation in the current paper is the nonlinear conformable time-fractional Zoomeron equation in (2 + 1)-dimensions, which is a model to display the novel phenomena associated with boomer...

... read more

Topics: Conformable matrix (62%), Nonlinear system (50%)

22 results found

Journal ArticleDOI: 10.1016/J.IJLEO.2020.165425
01 Dec 2020-Optik
Abstract: The main goal of the present paper is to steer an investigation on the dynamics of soliton solutions of a nonlinear model in the monomode optical fibers. In this respect, first, soliton solutions of the model termed as the Sasa–Satsuma (SS) equation describing the propagation of short light pulses are derived in the presence of the beta-derivatives; then, the dynamics of soliton solutions in the monomode optical fibers is analyzed for different values of the parameter β . The soliton solutions presented in this study are categorized in the most common classes of solitons namely bright and dark soliton solutions.

... read more

Topics: Soliton (62%)

41 Citations

Journal ArticleDOI: 10.1088/1555-6611/AB356F
Kamyar Hosseini1, Mohammad Mirzazadeh2, Qin Zhou, Yaxian Liu  +1 moreInstitutions (2)
02 Aug 2019-Laser Physics
Abstract: The ultrashort pulse propagation in optical metamaterials (OMMs) modeled by a generalized nonlinear Schrodinger equation with higher order effects is studied, in the present paper. To this end, by considering a complex envelope and a specific nonlinear chirp ansatz, a wide range of exact chirped soliton solutions are derived in the presence of the pseudo-quintic nonlinearity and the self-steepening effect. Exact solutions include kink and anti-kink chirped soliton solutions that are retrieved through the use of newly well-designed methods. The complex envelopes presented herein provide new specific nonlinear shock wave structures in OMMs which are vital for numerical and experimental verifications.

... read more

Topics: Ultrashort pulse (57%), Nonlinear Schrödinger equation (57%), Soliton (57%) ... read more

23 Citations

Journal ArticleDOI: 10.1016/J.CJPH.2019.11.003
Meryem Odabasi1Institutions (1)
Abstract: To model physical phenomena more accurately, fractional order differential equations have been widely used. Investigating exact solutions of the fractional differential equations have become more important because of the applications in applied mathematics, mathematical physics, and other areas. In this work, by means of the trial solution method and complete discrimination system, exact traveling wave solutions of the conformable time-fractional Zakharov–Kuznetsov equation and conformable time-fractional Zoomeron equation have been obtained and also solutions have been illustrated. Finding exact solutions of these equations that are encountered in plasma physics, nonlinear optics, fluid mechanics, and laser physics can help to understand nature of the complex phenomena.

... read more

19 Citations

Journal ArticleDOI: 10.1016/J.IJLEO.2020.164458
01 Apr 2020-Optik
Abstract: The current study is concerned with a (3 + 1)-dimensional resonant nonlinear Schrodinger (3D-RNLS) equation with diverse applications in nonlinear optics and its exact solutions. In this regard, by adopting the new expansion methods based on the Jacobi elliptic equation, a number of exact solutions in terms of Jacobi elliptic and exponential functions to the 3D-RNLS equation with Kerr law nonlinearity are formally constructed. The outcomes of this paper undoubtedly demonstrate the impressive capability of the new expansion methods to deal with nonlinear Schrodinger equations.

... read more

Topics: Nonlinear Schrödinger equation (58%), Nonlinear system (55%), Elliptic curve (54%) ... read more

17 Citations

Journal ArticleDOI: 10.1134/S156035472004005X
Kamyar Hosseini1, Majid Samavat2, Mohammad Mirzazadeh2, Wen-Xiu Ma  +1 moreInstitutions (2)
Abstract: The behavior of specific dispersive waves in a new $$(3+1)$$ -dimensional Hirota bilinear (3D-HB) equation is studied. A Backlund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painleve expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.

... read more

16 Citations


35 results found

Open accessJournal ArticleDOI: 10.1016/J.CAM.2014.01.002
Roshdi Khalil1, M. Al Horani1, A. Yousef1, Mohammad Sababheh2  +1 moreInstitutions (3)
Abstract: We give a new definition of fractional derivative and fractional integral. The form of the definition shows that it is the most natural definition, and the most fruitful one. The definition for [email protected][email protected]<1 coincides with the classical definitions on polynomials (up to a constant). Further, if @a=1, the definition coincides with the classical definition of first derivative. We give some applications to fractional differential equations.

... read more

1,390 Citations

Open accessJournal ArticleDOI: 10.1016/J.CNSNS.2011.10.016
Nikolay A. Kudryashov1Institutions (1)
Abstract: One of old methods for finding exact solutions of nonlinear differential equations is considered. Modifications of the method are discussed. Application of the method is illustrated for finding exact solutions of the Fisher equation and nonlinear ordinary differential equation of the seven order. It is shown that the method is one of the most effective approaches for finding exact solutions of nonlinear differential equations. Merits and demerits of the method are discussed.

... read more

440 Citations

Journal ArticleDOI: 10.1007/S10092-015-0158-8
Mostafa Eslami1, Hadi Rezazadeh2Institutions (2)
01 Sep 2016-Calcolo
Abstract: In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu---Zhang system. Fractional derivatives are described by conformable fractional derivative. This method is based on the ring theory of commutative algebra. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.

... read more

Topics: Fractional calculus (64%), Conformable matrix (59%), Partial differential equation (52%) ... read more

267 Citations

Journal ArticleDOI: 10.1080/17455030.2016.1205237
Abstract: In 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.

... read more

162 Citations

Journal ArticleDOI: 10.1080/17455030.2017.1296983
Kamyar Hosseini1, Reza Ansari2Institutions (2)
Abstract: In this paper, the nonlinear Boussinesq equations with the conformable time-fractional derivative are solved analytically using the well-established modified Kudryashov method. As a consequence, a number of new exact solutions for this type of equations are formally derived. It is believed that the method is one of the most effective techniques for extracting new exact solutions of nonlinear fractional differential equations.

... read more

Topics: Nonlinear system (59%)

107 Citations