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Journal ArticleDOI

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
TL;DR: In this article, the nonlinear conformable time-fractional Zoomeron equation in (2 + 1)-dimensions is investigated, which is a model to display the novel phenomena associated with boomer...
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...
Citations
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Journal ArticleDOI
01 Dec 2020-Optik
TL;DR: In this article, the Sasa-Satsuma (SS) equation describing the propagation of short light pulses is derived in the presence of the beta-derivatives, and the dynamics of soliton solutions in the monomode optical fibers is analyzed for different values of the parameter β.

71 citations

Journal ArticleDOI
01 Feb 2021-Optik
TL;DR: In this paper, an exact examination on the resonant nonlinear Schrodinger equation (RNLSE) with Kerr law nonlinearity considering inter-modal dispersion and spatio-temporal.

38 citations

Journal ArticleDOI
01 Mar 2021
TL;DR: The investigation of nematic liquid crystals, using the proposed method, shows that there is diversity between the solutions gained via this method with those obtained via different methods, and the constraint conditions to guarantee the existence of the solutions are used.
Abstract: In this work, we attempt to construct some novel solutions of nematicons within liquid crystals including three types of nonlinearity namely Kerr, parabolic, and power law, using the generalized exponential rational function method. The investigation of nematic liquid crystals, using the proposed method, shows that there is diversity between the solutions gained via this method with those obtained via different methods. Further, we use the constraint conditions to guarantee the existence of the solutions. The W-shaped surfaces, dark soliton, bright soliton, singular soliton, period singular soliton, periodic waves, and complex solutions of the studied equations are successfully constructed. Moreover, some obtained solutions are drawn to a better understanding of the characteristics of nematicons in liquid crystals.

34 citations

Journal ArticleDOI
TL;DR: In this paper, the behavior of specific dispersive waves in a new 3D-HB equation is studied and a Backlund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painleve expansion.
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.

29 citations

Journal ArticleDOI
TL;DR: In this article, the ultrashort pulse propagation in optical metamaterials (OMMs) modeled by a generalized nonlinear Schrodinger equation with higher order effects is studied, 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.
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.

28 citations

References
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Journal ArticleDOI
TL;DR: A new definition of fractional derivative and fractional integral is given and it is shown that it is the most natural definition, and the most fruitful one.

2,068 citations


"New wave form solutions of nonlinea..." refers background in this paper

  • ...Some noteworthy properties of this newly defined fractional derivative are summarized below [36,37]....

    [...]

  • ...The αth order of conformable derivative of the function f : [0,∞) → R is expressed as [36]...

    [...]

Journal ArticleDOI
TL;DR: In this article, a method for finding exact solutions of nonlinear differential equations is considered and modifications of the method are discussed, showing that the method is one of the most effective approaches for solving nonlinear problems.

569 citations

Journal ArticleDOI
01 Sep 2016-Calcolo
TL;DR: In this article, the first integral method was used to construct exact solutions of the Wu-Zhang system, which is based on the ring theory of commutative algebra, and 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.
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.

344 citations


"New wave form solutions of nonlinea..." refers background in this paper

  • ...Some noteworthy properties of this newly defined fractional derivative are summarized below [36,37]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative of the Burgers-Korteweg-de Vries equation.
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.

196 citations

Journal ArticleDOI
TL;DR: In this paper, the modified Kudryashov method was used to derive exact solutions for nonlinear Boussinesq equations with conformable time-fractional derivative.
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.

148 citations