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

2018 ◽  
Vol 33 (32) ◽  
pp. 1850183 ◽  
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.

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

2018 ◽  
Vol 33 (37) ◽  
pp. 1850217 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Dusty Plasma ◽  
Electrostatic Potential ◽  
Dynamical Equation ◽  
Graphical Representation ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
De Vries

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.

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

2019 ◽  
Vol 33 (18) ◽  
pp. 1950210 ◽  
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.

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

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
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.

scholarly journals Novel solitary wave solutions in parabolic law medium with weak non-local non-linearity

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 239-246
Author(s):  
Mostafa Khater ◽  
Raghda Attia ◽  
Sayed Elagan ◽  
Meteub Alharthi
Keyword(s):  
Solitary Wave ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Linear Dispersion ◽  
Auxiliary Equation Method ◽  
Wave Solutions ◽  
Parabolic Law ◽  
All Solutions ◽  
Non Linear ◽  
Non Local

In this paper, the auxiliary equation method is employed to construct novel solitary wave solutions of the dimensionless form of the non-linear Schrodinger equation with parabolic law of non-linearity in the presence of non-linear dispersion. The solutions are represented through various techniques to demonstrate the dynamical and physical behavior of the investigated models. All solutions are checked their accuracy by putting them back into the original model?s equation by MATHEMATICA 12.

Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation

2019 ◽  
Vol 34 (37) ◽  
pp. 1950309 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu ◽  
Xianwei Xia
Keyword(s):  
Solitary Wave ◽  
Perturbation Technique ◽  
Nonlinear Behavior ◽  
Physical Structure ◽  
Magnetized Plasma ◽  
Solitary Wave Solutions ◽  
Nonlinear Wave Propagation ◽  
Zk Equation ◽  
Dark Solitons ◽  
Wave Solutions

The nonlinear (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equations deal with the nonlinear behavior of waves in collision-less plasma, which contains non-isothermal cold ions and electrons. Two-dimensional dust acoustic solitary waves (DASWs) in magnetized plasma, which consist of trapped electrons and ions are leading to (2 + 1)-dim (ZK) equation by using the perturbation technique. We found the solitary wave solutions of (2 + 1)-dimensional (ZK)-equation, generalized (ZK)-equation and generalized form of modified (ZK)-equation by implementing the modified mathematical method. As a result, we obtained the bright–dark solitons, traveling wave and solitary wave solutions. The physical structure of obtained solutions is represented in 2D and 3D, graphically with the help of Mathematica.

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