On the rogue wave solution in the framework of a Korteweg–de Vries equation

Albalawi, Wedad; El-Tantawy, S. A.; Salas, Alvaro H.

doi:10.1016/j.rinp.2021.104847

Cited by 26 publications

(12 citation statements)

References 34 publications

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“…The derivative expansion method (DEM) is employed to obtain the NLSE. Accordingly, the following stretchings for the independent variables (x, t) and expansions for the dependent quantities are, respectively, introduced [32][33][34][35]74,75]:…”

Section: Nonlinear Schrödinger Equation and Modulational Instabilitymentioning

confidence: 99%

“…The coefficient of e iΘ for the third-mode (m = 3) gives the compatibility condition and the solution of this condition leads to the following NLSE [32][33][34][35]…”

Section: Nonlinear Schrödinger Equation and Modulational Instabilitymentioning

confidence: 99%

“…The dynamical behaviors of the symmetric arbitrary amplitude unmodulated EASWs have been studied via the Sagdeev potential approach [31], where the dynamics of the solitary pulses are determined through an energy integral equation and the existence domain of the solitons could be estimated from the maximum and minimum Mach numbers. On the contrary, the modulationally unstable region and the propagation of modulated waves can be analyzed by deriving a nonlinear Schrödinger equation (NLSE) [32][33][34][35][36][37][38]. These modulated structures include rogue waves (RWs), i.e., Peregrine soliton (first-order RW) [39], and higher-order RWs (super RWs) [40,41], as well as the breathers, i.e., Akhmediev breathers (ABs) [42], and the Kuznetsov-Ma (KM) soliton [43,44], which can be investigated using the derivative expansion method (DEM).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

et al. 2021

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The propagation of electron-acoustic waves (EAWs) in an unmagnetized plasma, comprising (r,q)-distributed hot electrons, cold inertial electrons, and stationary positive ions, is investigated. Both the unmodulated and modulated EAWs, such as solitary waves, rogue waves (RWs), and breathers are discussed. The Sagdeev potential approach is employed to determine the existence domain of electron acoustic solitary structures and study the perfectly symmetric planar nonlinear unmodulated structures. Moreover, the nonlinear Schrödinger equation (NLSE) is derived and its modulated solutions, including first order RWs (Peregrine soliton), higher-order RWs (super RWs), and breathers (Akhmediev breathers and Kuznetsov–Ma soliton) are presented. The effects of plasma parameters and, in particular, the effects of spectral indices r and q, of distribution functions on the characteristics of both unmodulated and modulated EAWs, are examined in detail. In a limited cases, the (r,q) distribution is compared with Maxwellian and kappa distributions. The present investigation may be beneficial to comprehend and predict the modulated and unmodulated electron acoustic structures in laboratory and space plasmas.

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Section: Nonlinear Schrödinger Equation and Modulational Instabilitymentioning

confidence: 99%

“…The coefficient of e iΘ for the third-mode (m = 3) gives the compatibility condition and the solution of this condition leads to the following NLSE [32][33][34][35]…”

Section: Nonlinear Schrödinger Equation and Modulational Instabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

et al. 2021

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“…Therefore, it is important to be familiar with all recent analytical and numerical methods for modeling any natural and physical problem and solving it [1][2][3][4][5][6]. The following Korteweg-De Vries equation (KdV) equation is one of the most famous PDEs that has gained fame during the more than 50 years since its creation due to its ability for modeling many physical and natural phenomena in various fields of science [2,7] ∂ t ϕ + αϕ∂ x ϕ + β∂ 3 x ϕ = 0, (1) where ϕ ≡ ϕ(x, t) and α represents the coefficient of the nonlinear term, while β refers to the coefficient of the dispersion term. The coefficients (α, β) are the function of physical parameters related to the model under consideration.…”

Section: Introductionmentioning

confidence: 99%

New Localized and Periodic Solutions to a Korteweg–de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models

2022

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Traveling wave solutions, including localized and periodic structures (e.g., solitary waves, cnoidal waves, and periodic waves), to a symmetry Korteweg–de Vries equation (KdV) with integer and rational power law nonlinearity are reported using several approaches. In the case of the localized wave solutions, i.e., solitary waves, to the evolution equation, two different methods are devoted for this purpose. In the first one, new hypotheses with Cole–Hopf transformation are employed to find general solitary wave solutions. In the second one, the ansatz method with hyperbolic sech algorithm are utilized to obtain a general solitary wave solution. The obtained solutions recover the solitary wave solutions to all one-dimensional KdV equations with a power law nonlinearity, such as the KdV equation with quadratic nonlinearity, the modified KdV (mKdV) equation with cubic nonlinearity, the super KdV equation with quartic nonlinearity, and so on. Furthermore, two different approaches with two different formulas for the Weierstrass elliptic functions (WSEFs) are adopted for deriving some general periodic wave solutions to the evolution equation. Additionally, in the form of Jacobi elliptic functions (JEFs), the cnoidal wave solutions to the KdV-, mKdV-, and SKdV equations are obtained. These results help many authors to understand the mystery of several nonlinear phenomena in different branches of sciences, such as plasma physics, fluid mechanics, nonlinear optics, Bose Einstein condensates, and so on.

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“…A large number of researchers have studied the dynamics of the IAWs experimentally and theoretically in the last few decades [3][4][5][6][7][8][9][10]. There are many approaches for investigation the different types of nonlinear structures in plasma physics such as a reductive perturbation technique (RPT), Sagdeev potential approach, etc.…”

Section: Introductionmentioning

confidence: 99%

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

et al. 2021

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In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems.

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On the rogue wave solution in the framework of a Korteweg–de Vries equation

Cited by 26 publications

References 34 publications

Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

Electron-Acoustic (Un)Modulated Structures in a Plasma Having (r, q)-Distributed Electrons: Solitons, Super Rogue Waves, and Breathers

New Localized and Periodic Solutions to a Korteweg–de Vries Equation with Power Law Nonlinearity: Applications to Some Plasma Models

Linear and Nonlinear Electrostatic Excitations and Their Stability in a Nonextensive Anisotropic Magnetoplasma

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