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Aly R Seadawy - One of the best experts on this subject based on the ideXlab platform.
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construction of soliton solutions of the modify unstable nonlinear schrodinger dynamical Equation in fiber optics
Indian Journal of Physics, 2020Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:In this research article, we investigated the universal model of integrable system of modify unstable nonlinear Schrodinger Equation. The mUNLSE described the disturbance of time period in slightly stable and unstable media and managed the instability of modulation wave train. We found the exact and solitary wave solutions of mUNLSE with the help of modified extended Auxiliary Equation mapping method. As a result, exact and solitary wave solutions in the form of elliptic functions, trigonometric functions, hyperbolic functions, bright and dark solitons, traveling wave, kink-type solitons and periodic solitary wave solution are obtained. These solutions show the power and effectiveness of this new method and two- and three-dimensional graphically with the help of computer software Mathematica. We can also solve other unstable nonlinear system of PDEs which are involved in Mathematical physics and many other branches of physical sciences with the help of this new method.
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applications of propagation of long wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized kadomtsev petviashvili modified equal width dynamical Equation
Computers & Mathematics With Applications, 2019Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:Abstract In this research work, we constructed the solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width (KP-MEW) Equation with the help of new technique which is modification form of extended Auxiliary Equation mapping method. The generalized KP-MEW Equation is the nonlinear PDEs which described the propagation of long-wave with dissipation and dispersion in nonlinear media. As a result, families of solitary wave solutions are obtained in different form of solitons, bright–dark solitons and traveling wave solutions. The physical structure of these new solutions is shown graphically in two and three dimensions with the aid of computer software Mathematica. These obtained new solutions show the power and effectiveness of this new method. We can also solve other nonlinear system of PDEs which are involved in mathematical physics and many other branches of physical sciences with the help of this new method.
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application of mathematical methods on the system of dynamical Equations for the ion sound and langmuir waves
Pramana, 2019Co-Authors: Aly R Seadawy, Dianchen Lu, Mujahid IqbalAbstract:We investigated the new exact travelling wave solutions of the system of Equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, Auxiliary Equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs. We used the Mathematica program to show these solutions in two and three dimensions graphically.
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applications of extended modified Auxiliary Equation mapping method for high order dispersive extended nonlinear schrodinger Equation in nonlinear optics
Modern Physics Letters B, 2019Co-Authors: Aly R Seadawy, Nadia CheemaaAbstract:In this paper, we discussed analytically higher order dispersive extended nonlinear Schrodinger Equation with the aid of newly developed technique named as extended modified Auxiliary Equation mapp...
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dispersive solitary wave solutions of nonlinear further modified korteweg de vries dynamical Equation in an unmagnetized dusty plasma
Modern Physics Letters A, 2018Co-Authors: Mujahid Iqbal, Aly R SeadawyAbstract:In this work, we consider the propagation of one-dimensional nonlinear unmagnetized dusty plasma, by using the reductive perturbation technique to formulate the nonlinear mathematical model which is further modified Korteweg–de Vries (fmKdV) dynamical Equation. We use the extend form of two methods, Auxiliary Equation mapping and direct algebraic methods, to investigate the families of dust and ion solitary wave solutions of one-dimensional nonlinear fmKdV. These new exact and solitary wave solutions, which represent the electrostatic potential and pressure for fmKdV, and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica.
Turgut Öziş - One of the best experts on this subject based on the ideXlab platform.
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observations on the class of balancing principle for nonlinear pdes that can be treated by the Auxiliary Equation method
Nonlinear Analysis-real World Applications, 2015Co-Authors: Zehra Pinar, Turgut ÖzişAbstract:Abstract There is collection of methods for finding explicit travelling wave solutions of nonlinear partial differential Equations (NLPDEs) in the literature. Quite a large amount of these methods employ “Balancing Principle” in their methodology and they work for positive integer values only. Yet there is no well established formula for balancing and there is no specific rule to determine adequate balancing principle that works for any number which is positive/or negative and/or rational. In this study, we propose a new balancing principle which works for large range of the numbers either positive/or negative and/or rational that makes it possible to obtain new and original explicit travelling wave solutions of nonlinear partial differential Equations (NLPDEs).
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analytical solution of population balance Equation involving growth nucleation and aggregation in terms of Auxiliary Equation method
Applied Mathematics & Information Sciences, 2015Co-Authors: Zehra Pinar, Abhishek Dutta, Guido Beny, Turgut ÖzişAbstract:The Auxiliary Equation Method (AEM) has been modified to obtain the solutions of a Population Balance Equation (PBE) involving particulate growth, nucleation and aggregation phenomena. In all the cases examined, the volume density distributions are accurately predicted by the travelling wave solutions of the complementary Equation of the nonlinear partial integro-differential Equation with distinctly chosen parameters. Being a flexible techniq ue and a direct comparison for the existing analytical solut ions, this study proves the potential of the proposed methodology.
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analytical solution of population balance Equation involving aggregation and breakage in terms of Auxiliary Equation method
Pramana, 2015Co-Authors: Zehra Pinar, Abhishek Dutta, Guido Beny, Turgut ÖzişAbstract:This paper presents an effective analytical simulation to solve population balance Equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary Equation via Auxiliary Equation method (AEM). Travelling wave solutions of the complementary Equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and thereby more efficient than the analytical approach used in the literature.
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The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term
Journal of Mathematics, 2013Co-Authors: Zehra Pinar, Turgut ÖzişAbstract:It is well known that different types of exact solutions of an Auxiliary Equation produce new types of exact travelling wave solutions to nonlinear Equations. In this paper, by means of symbolic computation, the new solutions of original Auxiliary Equation of first-order nonlinear ordinary differential Equation with a sixth-degree nonlinear term are presented to obtain novel exact solutions of the Kawahara Equation. By the aid of the solutions of the original Auxiliary Equation, some other physically important nonlinear Equations can be solved to construct novel exact solutions.
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An observation on the periodic solutions to nonlinear physical models by means of the Auxiliary Equation with a sixth-degree nonlinear term
Communications in Nonlinear Science and Numerical Simulation, 2013Co-Authors: Zehra Pinar, Turgut ÖzişAbstract:Abstract It is a fact that in Auxiliary Equation methods, the exact solutions of different types of Auxiliary Equations may produce new types of exact travelling wave solutions to nonlinear Equations. In this manner, various Auxiliary Equations of first-order nonlinear ordinary differential Equation with distinct-degree nonlinear terms are examined and, by means of symbolic computation, the new solutions of original Auxiliary Equation of first-order nonlinear ordinary differential Equation with sixth-degree nonlinear term are presented. Consequently, the novel exact solutions of the generalized Klein–Gordon Equation and the active-dissipative dispersive media Equation are found out for illustration purposes. They are also applicable, where conventional perturbation method fails to provide any solution of the nonlinear problems under study.
Li-jiang Chen - One of the best experts on this subject based on the ideXlab platform.
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comment on an observation on the periodic solutions to nonlinear physical models by means of the Auxiliary Equation with a sixth degree nonlinear term commun nonlinear sci numer simulat 2013 18 2177 2187
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: Hong-zhun Liu, Xiao-quan Sun, Li-jiang ChenAbstract:Abstract This article shows that all novel exact solutions in the commented paper are not admitted by the original generalized Klein–Gordon Equation and active-dissipative dispersive media Equation. In addition, we present general solutions of certain Auxiliary Equation with sixth-degree nonlinear term. Then, based on above general solutions, we find that five cases in their Table 1 is shown to be incorrect.
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Comment on: “An observation on the periodic solutions to nonlinear physical models by means of the Auxiliary Equation with a sixth-degree nonlinear term” [Commun Nonlinear Sci Numer Simulat 2013;18:2177–2187]
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: Hong-zhun Liu, Xiao-quan Sun, Li-jiang ChenAbstract:Abstract This article shows that all novel exact solutions in the commented paper are not admitted by the original generalized Klein–Gordon Equation and active-dissipative dispersive media Equation. In addition, we present general solutions of certain Auxiliary Equation with sixth-degree nonlinear term. Then, based on above general solutions, we find that five cases in their Table 1 is shown to be incorrect.
Zehra Pinar - One of the best experts on this subject based on the ideXlab platform.
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the combination of conservation laws and Auxiliary Equation method
International Journal of Applied and Computational Mathematics, 2020Co-Authors: Zehra PinarAbstract:In this paper, appropriate Lie group transformations are considered as an alternative to a travelling wave transformation, in the Auxiliary Equation method to solve the nonlinear partial differential Equations. In addition, Bernoulli differential Equation has been considered as an Auxiliary Equation and using the approach presented.
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observations on the class of balancing principle for nonlinear pdes that can be treated by the Auxiliary Equation method
Nonlinear Analysis-real World Applications, 2015Co-Authors: Zehra Pinar, Turgut ÖzişAbstract:Abstract There is collection of methods for finding explicit travelling wave solutions of nonlinear partial differential Equations (NLPDEs) in the literature. Quite a large amount of these methods employ “Balancing Principle” in their methodology and they work for positive integer values only. Yet there is no well established formula for balancing and there is no specific rule to determine adequate balancing principle that works for any number which is positive/or negative and/or rational. In this study, we propose a new balancing principle which works for large range of the numbers either positive/or negative and/or rational that makes it possible to obtain new and original explicit travelling wave solutions of nonlinear partial differential Equations (NLPDEs).
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analytical solution of population balance Equation involving growth nucleation and aggregation in terms of Auxiliary Equation method
Applied Mathematics & Information Sciences, 2015Co-Authors: Zehra Pinar, Abhishek Dutta, Guido Beny, Turgut ÖzişAbstract:The Auxiliary Equation Method (AEM) has been modified to obtain the solutions of a Population Balance Equation (PBE) involving particulate growth, nucleation and aggregation phenomena. In all the cases examined, the volume density distributions are accurately predicted by the travelling wave solutions of the complementary Equation of the nonlinear partial integro-differential Equation with distinctly chosen parameters. Being a flexible techniq ue and a direct comparison for the existing analytical solut ions, this study proves the potential of the proposed methodology.
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analytical solution of population balance Equation involving aggregation and breakage in terms of Auxiliary Equation method
Pramana, 2015Co-Authors: Zehra Pinar, Abhishek Dutta, Guido Beny, Turgut ÖzişAbstract:This paper presents an effective analytical simulation to solve population balance Equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary Equation via Auxiliary Equation method (AEM). Travelling wave solutions of the complementary Equation of a nonlinear PBE with appropriately chosen parameters is taken to be analogous to the description of the dynamic behaviour of the particulate processes. For an initial proof-of-concept, a general case when the number of particles varies with respect to time is chosen. Three cases, i.e. (1) balanced aggregation and breakage, (2) when aggregation can dominate and (3) breakage can dominate, are selected and solved for their corresponding analytical solutions. The results are then compared with the available analytical solution, based on Laplace transform obtained from literature. In this communication, it is shown that the solution approach proposed via AEM is flexible and thereby more efficient than the analytical approach used in the literature.
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The Periodic Solutions to Kawahara Equation by Means of the Auxiliary Equation with a Sixth-Degree Nonlinear Term
Journal of Mathematics, 2013Co-Authors: Zehra Pinar, Turgut ÖzişAbstract:It is well known that different types of exact solutions of an Auxiliary Equation produce new types of exact travelling wave solutions to nonlinear Equations. In this paper, by means of symbolic computation, the new solutions of original Auxiliary Equation of first-order nonlinear ordinary differential Equation with a sixth-degree nonlinear term are presented to obtain novel exact solutions of the Kawahara Equation. By the aid of the solutions of the original Auxiliary Equation, some other physically important nonlinear Equations can be solved to construct novel exact solutions.
Mostafa M A Khater - One of the best experts on this subject based on the ideXlab platform.
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dispersive long wave of nonlinear fractional wu zhang system via a modified Auxiliary Equation method
AIP Advances, 2019Co-Authors: Mostafa M A Khater, Raghda A M AttiaAbstract:In this paper, we examine a modified Auxiliary Equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential Equations. We used conformable derivatives properties to convert nonlinear fractional partial differential Equation into the ordinary differential Equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.In this paper, we examine a modified Auxiliary Equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential Equations. We used conformable derivatives properties to convert nonlinear fractional partial differential Equation into the ordinary differential Equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.
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dispersive long wave of nonlinear fractional wu zhang system via a modified Auxiliary Equation method
AIP Advances, 2019Co-Authors: Mostafa M A Khater, Raghda A M AttiaAbstract:In this paper, we examine a modified Auxiliary Equation method. We applied this novel method on Wu-Zhang system. This model used to describe (1 + 1)-dimensional dispersive long wave in two horizontal directions on shallow waters. This model is one of the fractional nonlinear partial differential Equations. We used conformable derivatives properties to convert nonlinear fractional partial differential Equation into the ordinary differential Equation with integer order. We obtained many different kinds of solutions such as kink and anti-kink, dark, bright, shock, singular, periodic solitary wave.
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Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation
Mathematical and Computational Applications, 2019Co-Authors: Raghda A M Attia, Mostafa M A KhaterAbstract:This paper studies the nonlinear fractional undamped Duffing Equation. The Duffing Equation is one of the fundamental Equations in engineering. The geographical areas of this model represent chaos, relativistic energy-momentum, electrodynamics, and electromagnetic interactions. These properties have many benefits in different science fields. The Equation depicts the energy of a point mass, which is well thought out as a periodically-forced oscillator. We employed twelve different techniques to the nonlinear fractional Duffing Equation to find explicit solutions and approximate solutions. The stability of the solutions was also examined to show the ability of our obtained solutions in the application. The main goals here were to apply a novel computational method (modified Auxiliary Equation method) and compare the novel method with other methods via the solutions that were obtained by each of these methods.
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modified Auxiliary Equation method versus three nonlinear fractional biological models in present explicit wave solutions
Mathematical & Computational Applications, 2018Co-Authors: Mostafa M A Khater, Raghda A M AttiaAbstract:In this article, we present a modified Auxiliary Equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width Equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential Equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential Equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original Equations via computer software such as Maple, Mathematica, and Matlab.
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dispersive optical soliton solutions of the generalized radhakrishnan kundu lakshmanan dynamical Equation with power law nonlinearity and its applications
Optik, 2018Co-Authors: Aly R Seadawy, Mostafa M A KhaterAbstract:Abstract In this research, we study the generalized Radhakrishnan–Kundu–Lakshmanan Equation which describe the dynamics of light pulses and it is also described by the nonlinear Schrodinger family of Equations with cubic nonlinear terms. We use two Auxiliary Equation methods (extended simple Equation method and new Auxiliary Equation method)) to obtain the exact and solitary traveling wave solutions of this model. We get new form of solitary traveling wave solutions for this model which help the researchers who interested in the applications of this model to be able to study the physical properties of the model.