Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics

Kumar, Sachin; Almusawa, Hassan; Hamid, Ihsanullah; Abdou, Mohamed

doi:10.1016/j.rinp.2021.104453

Cited by 66 publications

(14 citation statements)

References 34 publications

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“…A large number of researchers and mathematicians have developed various effective techniques for computing exact solutions of NLPDEs (nonlinear partial differential equations), for instance, tanh function method [1], Hirota's bilinear method [2,3], the Jacobi elliptic function expansion method [4], Kudryashov method [5], the G ′ G -expansion method [6], Darboux transformation method [7], the Backlund transformation method [8], the inverse scattering method [9], Lie-symmetry analysis [10], multiple exp-function method, and many others. Among these techniques, GERF method [11][12][13][14] is very effective, robust and straightforward approach for finding the abundant exact soliton-form solutions of various NLPDEs.…”

Section: Introduction 1aims and Scopementioning

confidence: 99%

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

et al. 2023

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Nonlinear evolution equations (NLEEs) are extensively used to establish the elementary propositions of natural circumstances. In this work, we study the Konopelchenko-Dubrovsky (KD) equation which depicts non-linear waves in mathematical physics with weak dispersion. The considered model is investigated using the combination of generalized exponential rational function (GERF) method and dynamical system method. The GERF method is utilized to generate closed-form invariant solutions to the (2+1)-dimensional KD model in terms of trigonometric, hyperbolic, and exponential forms with the assistance of symbolic computations. Moreover, 3D, 2D combined line graph and their contour graphics are displayed to depict the behavior of obtained solitary wave solutions. The model is observed to have multiple soliton profiles, kink-wave profiles, and periodic oscillating nonlinear waves. These generated solutions have never been published in the literature. All the newly generated soliton solutions are checked by putting them back into the associated system with the soft computation via Wolfram Mathematica. Moreover, the system is converted into a planer dynamical system using a certain transformation and the analysis of bifurcation is examined. Furthermore, the quasi-periodic solution is investigated numerically for the perturbed system by inserting definite periodic forces into the considered model. With regard to the parameter of the perturbed model, two-dimensional and three-dimensional phase portraits are plotted.

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Section: Introduction 1aims and Scopementioning

confidence: 99%

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

et al. 2023

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“…Exp-function method, 10 Bernoulli sub-equation function method, 11 F-expansion method, 12 energy balance method, 13 the direct mapping method, 14 1=G 0 À Á -expansion method, 15 and so on. [16][17][18][19][20][21][22][23][24][25][26][27][28][29] We considered the coupled Higgs field equation (CHFE), which is important in nucleus theory. 30 u tt À u xx À αu þ βjuj 2 u À 2uv ¼ 0,…”

Section: Introductionmentioning

confidence: 99%

Traveling wave and general form solutions for the coupled Higgs system

Duran

Durur

Yokuş

2023

Math Methods in App Sciences

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In this study, the coupled Higgs system, which is a special case of the coupled Higgs field equation, which is effective in energy transport in the sub-particles of the atom, is discussed. With the help of the modified generalized exponential rational function method, which is an important instrument in obtaining traveling wave solutions, both the propagating wave solutions and general form solutions of coupled Higgs system are presented. These solutions are examined under some restrictive conditions as they are presented. It is argued that these solutions differ from the literature. The advantages and disadvantages of the method discussed in the conclusion and discussion section are discussed. In addition, the changes in the behavior of the traveling wave solution are discussed by giving physical meaning to some constants in the traveling wave solutions produced by the method. The effects on the traveling wave solution are analyzed for different values of wave number, wave velocity, and wave frequency, which have physically important meanings. In addition, the behaviors caused by these effects are supported with the help of simulation.

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“…The nonlinear evolution models are used to mimic the effect of surface for deep water and weakly nonlinear dispersive long waves in the presence of solitary waves. Therefore, the precise solutions of such models are essential for understanding dynamical structures and additional characteristics of physical phenomena that occur in many domains, including geophysics, physical chemistry, electromagnetic, Nuclear physics, electrochemistry, optical fibers, energy physics, chemical mechanics, gravitation, biostatistics, statistical, and natural physics, as well as ionized physics, elastic medium, fluid motion, fluid mechanics, and elastic medium 1–6 …”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the precise solutions of such models are essential for understanding dynamical structures and additional characteristics of physical phenomena that occur in many domains, including geophysics, physical chemistry, electromagnetic, Nuclear physics, electrochemistry, optical fibers, energy physics, chemical mechanics, gravitation, biostatistics, statistical, and natural physics, as well as ionized physics, elastic medium, fluid motion, fluid mechanics, and elastic medium. [1][2][3][4][5][6] Solitons play a critical role in understanding the nonlinear phenomenon of many important structures thanks to recent advancements in a variety of modern analytical approaches. The primary characteristic of solitons is that they nearly always take on the same shapes and velocities after colliding, and the generation of optical solitons is correlated with optical frequency.…”

Section: Introductionmentioning

confidence: 99%

Some traveling wave solutions to the generalized (3 + 1)‐dimensional Korteweg–de Vries–Zakharov–Kuznetsov equation in plasma physics

Tariq

Javed

2022

Math Methods in App Sciences

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The generalized Korteweg-de Vries-Zakharov-Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion-acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F-expansion approach and the exp(−𝜙(𝜁))-expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell-shaped, and single bell-shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. KEYWORDS exact wave solutions, improved F-expansion method, stability analysis, the (3 + 1)-dimensional gKdV-ZK model, the exp(−𝜙(𝜁 ))-expansion technique, traveling waves solutions MSC CLASSIFICATION

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Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics

Cited by 66 publications

References 34 publications

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

Dynamical behavior of analytical soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+1)-dimensional Konopelchenko–Dubrovsky (KD) system

Traveling wave and general form solutions for the coupled Higgs system

Some traveling wave solutions to the generalized (3 + 1)‐dimensional Korteweg–de Vries–Zakharov–Kuznetsov equation in plasma physics

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