Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

Abstract The nonlinear propagation of ion-acoustic (IA) electrostatic solitary waves (SWs) is studied in a magnetized electron–ion (e–i) plasma in the presence of pressure anisotropy with electrons following Tsallis distribution. The Korteweg–de Vries (KdV) type equation is derived by employing the reductive perturbation method (RPM) and its solitary wave (SW) solution is determined and analyzed. The effect of nonextensive parameter q, parallel component of anisotropic ion pressure p 1, perpendicular component of anisotropic ion pressure p 2, obliqueness angle θ, and magnetic field strength Ω on the characteristics of SW structures is investigated. The present investigation could be useful in space and astrophysical plasma systems.

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Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-01-2019-0047 ◽

2019 ◽

Vol 29 (8) ◽

pp. 2964-2976

Author(s):

Hui Wang ◽

Shou-Fu Tian ◽

Yi Chen

Keyword(s):

Solitary Waves ◽

Dynamical Behavior ◽

Rogue Waves ◽

Graphical Analysis ◽

Nonlinear Phenomena ◽

Kp Equation ◽

Bilinear Method ◽

Test Technique ◽

Content Type ◽

Petviashvili Equation

Purpose The purpose of this paper is to study the breather waves, rogue waves and solitary waves of an extended (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation, which can be used to depict many nonlinear phenomena in fluid dynamics and plasma physics. Design/methodology/approach The authors apply the Bell’s polynomial approach, the homoclinic test technique and Hirota’s bilinear method to find the breather waves, rogue waves and solitary waves of the extended (3 + 1)-dimensional KP equation. Findings The results imply that the extended (3 + 1)-dimensional KP equation has breather wave, rogue wave and solitary wave solutions. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior. Originality/value These results may help us to further study the local structure and the interaction of solutions in KP-type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of such equations.

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Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev–Petviashvili equation

Modern Physics Letters B ◽

10.1142/s021798491750350x ◽

2017 ◽

Vol 31 (36) ◽

pp. 1750350 ◽

Cited By ~ 2

Author(s):

Xue-Wei Yan ◽

Shou-Fu Tian ◽

Min-Jie Dong ◽

Li Zou

Keyword(s):

Solitary Waves ◽

Water Waves ◽

Variable Coefficient ◽

Wave Equations ◽

Direct Method ◽

Dynamical Behavior ◽

Rogue Waves ◽

Nonlinear Wave Equations ◽

Quasiperiodic Solutions ◽

Petviashvili Equation

In this paper, the generalized variable-coefficient forced Kadomtsev–Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

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