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.

scholarly journals New and more dual-mode solitary wave solutions for the Kraenkel-Manna-Merle system incorporating fractal effects

2021 ◽  
Author(s):  
Nauman Raza ◽  
Zara Hassan ◽  
Asma Butt ◽  
Riaz Rahman ◽  
Abdel-Haleem Abdel-Aty
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Short Wave ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Dual Mode ◽  
Auxiliary Equation Method ◽  
Wave Solutions ◽  
Contour Plots ◽  
Exact Soliton Solutions

This paper introduces the fractal Kraenkel-Manna-Merle (KMM) system, that explains nonlinear short wave propagation with zero conductivity for saturated ferromagnetic materials in an external field. The semi inverse technique and the new auxiliary equation method (NAEM) are used to generate a new set of solutions. The proposed methods are more straightforward, succinct, accurate, and simple to calculate dual mode solitary wave solutions. A collection of exact soliton solutions specifically bright, dark, singular-shaped and singular-periodic are generated. The estimated solutions are obtained using constraint conditions and are displayed through 2D, 3D and contour plots with appropriate parametric values. The arbitrary functions in the solutions are chosen as unique functions to generate some novel soliton structures.

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.

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.

SPATIAL SOLITARY WAVES IN GENERALIZED NON-LOCAL NONLINEAR MEDIA

2010 ◽  
Vol 19 (02) ◽  
pp. 311-317 ◽  
Author(s):  
WEI-PING ZHONG ◽  
ZHENG-PING YANG
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Cylindrical Coordinates ◽  
Intensity Pattern ◽  
Nonlinear Media ◽  
Wave Solutions ◽  
Non Local

We introduce a very general self-trapped beam solution to the generalized non-local nonlinear Schrödinger equation in cylindrical coordinates, by combining superpositions of the known single accessible soliton solutions. Specific values of soliton parameters are selected as initial conditions and superpositions of the single soliton solutions in the highly non-local regime are launched into the non-local nonlinear medium with Gaussian response function, to obtain novel numerical solitary wave solutions. Novel solitary waves have been constructed that exhibit unique features whose intensity pattern is formed by various figures.

scholarly journals Study on the solitary wave solutions of the ionic currents on microtubules equation by using the modified Khater method

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2053-2062 ◽  
Author(s):  
Jing Li ◽  
Yuyang Qiu ◽  
Dianchen Lu ◽  
Raghda Attia ◽  
Mostafa Khater
Keyword(s):  
Solitary Wave ◽  
Ionic Current ◽  
Ionic Currents ◽  
Solitary Wave Solutions ◽  
Linear Partial Differential Equations ◽  
Wave Solutions ◽  
Non Linear ◽  
The Stability ◽  
Main Components ◽  
And Function

In this survey, the ionic current along microtubules equation is handled by applying the modified Khater method to get the solitary wave solutions that describe the ionic transport throughout the intracellular environment which describes the behavior of many applications in a biological non-linear dispatch line for ionic currents. The obtained solutions support many researchers who are concerned with the discussion of the physical properties of the ionic currents along microtubules. Microtubules are one of the main components of the cytoskeleton, and function in many operations, comprehensive constitutional backing, intracellular transmit, and DNA division. Moreover, we also study the stability property of our obtained solutions. All obtained solutions are verified by backing them into the original equation by using MAPLE 18 and MATHEMATICA 11.2. These solutions show the power and effective of the used method and its ability for applying to many other different forms of non-linear partial differential equations.

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.

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