Dispersive solitary wave solutions of nonlinear further modified Korteweg–de Vries dynamical equation in an unmagnetized dusty plasma

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.

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Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods

Modern Physics Letters A ◽

10.1142/s0217732318501833 ◽

2018 ◽

Vol 33 (32) ◽

pp. 1850183 ◽

Cited By ~ 44

Author(s):

Mujahid Iqbal ◽

Aly R. seadawy ◽

Dianchen Lu

Keyword(s):

Solitary Wave ◽

Electrostatic Potential ◽

Graphical Representation ◽

Perturbation Technique ◽

Mathematic Model ◽

Auxiliary Equation ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

De Vries ◽

Unmagnetized Plasma

In this research, we consider the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma. By using the reductive perturbation technique to formulate the nonlinear mathematic model which is modified Kortewege-de Vries (mKdV), we apply the extended form of two methods, which are extended auxiliary equation mapping and extended direct algebraic methods, to investigate the new families of electron-acoustic solitary wave solutions of mKdV. These new exact traveling and solitary wave solutions which represent the electrostatic potential for mKdV and also the graphical representation of electrostatic potential are shown with the aid of Mathematica.

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Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions

Modern Physics Letters B ◽

10.1142/s0217984919502105 ◽

2019 ◽

Vol 33 (18) ◽

pp. 1950210 ◽

Cited By ~ 17

Author(s):

Mujahid Iqbal ◽

Aly R. Seadawy ◽

Dianchen Lu

Keyword(s):

Wave Equation ◽

Solitary Wave ◽

Longitudinal Wave ◽

Electrostatic Potential ◽

Graphical Representation ◽

Algebraic Method ◽

Hyperbolic Function ◽

Auxiliary Equation ◽

Solitary Wave Solutions ◽

Wave Solutions

In this work, we consider the nonlinear longitudinal wave equation (LWE) which involves mathematical physics with dispersal produced by the phenomena of transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod. We use the extended form of two methods, auxiliary equation mapping and direct algebraic method to investigated the families of solitary wave solutions of one-dimensional nonlinear LWE. These new exact and solitary wave solutions are derived in the form of trigonometric function, periodic solitary wave, rational function, and elliptic function, hyperbolic function, bright and dark solitons solutions of the LWE, which represent the electrostatic potential and pressure for LWE and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica program.

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Three-Dimensional Nonlinear Extended Zakharov-Kuznetsov Dynamical Equation in a Magnetized Dusty Plasma via Acoustic Solitary Wave Solutions

Brazilian Journal of Physics ◽

10.1007/s13538-018-0617-1 ◽

2018 ◽

Vol 49 (1) ◽

pp. 67-78 ◽

Cited By ~ 16

Author(s):

Abdullah ◽

Aly R. Seadawy ◽

Jun Wang

Keyword(s):

Solitary Wave ◽

Dusty Plasma ◽

Dynamical Equation ◽

Three Dimensional ◽

Solitary Wave Solutions ◽

Magnetized Dusty Plasma ◽

Wave Solutions

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Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma

Results in Physics ◽

10.1016/j.rinp.2016.08.023 ◽

2016 ◽

Vol 6 ◽

pp. 590-593 ◽

Cited By ~ 89

Author(s):

Aly R. Seadawy ◽

Dianchen Lu

Keyword(s):

Solitary Wave ◽

Dusty Plasma ◽

Dynamical Equation ◽

Three Dimensional ◽

Solitary Wave Solutions ◽

Ion Temperature ◽

Wave Solutions ◽

Ion Acoustic

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Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽

10.1515/phys-2018-0111 ◽

2018 ◽

Vol 16 (1) ◽

pp. 896-909 ◽

Cited By ~ 16

Author(s):

Dianchen Lu ◽

Aly R. Seadawy ◽

Mujahid Iqbal

Keyword(s):

Solitary Wave ◽

Nonlinear Partial Differential Equations ◽

Research Work ◽

Traveling Wave Solutions ◽

Elliptic Functions ◽

Mapping Method ◽

New Method ◽

Auxiliary Equation ◽

Solitary Wave Solutions ◽

Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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