scholarly journals Approximate Analytical Solution of Nonlinear Evolution Equations

2020 ◽  
Author(s):  
Laxmikanta Mandi ◽  
Kaushik Roy ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Nonlinear Evolution Equations ◽  
Charged Dust ◽  
De Vries ◽  
Frame Work ◽  
Dust Grain ◽  
Charged Ions

Analytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the frame-work of Korteweg-de Vries (KdV), damped force Korteweg-de Vries (DFKdV), damped force modified Korteweg-de Vries (DFMKdV) and damped forced Zakharov-Kuznetsov (DFZK) equations in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, Maxwellian distributed electrons and neutral particles. Using reductive perturbation technique (RPT), the evolution equations are obtained for DIAWs.

Effect of Dust Ion Collision on Dust Ion Acoustic Solitary Waves for Nonextensive Plasmas in the Framework of Damped Korteweg–de Vries–Burgers Equation

2019 ◽  
Vol 74 (10) ◽  
pp. 861-867 ◽  
Author(s):  
Niranjan Paul ◽  
Kajal Kumar Mondal ◽  
Prasanta Chatterjee
Keyword(s):  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Viscosity Coefficient ◽  
Travelling Wave ◽  
Physical Parameters ◽  
Charged Dust ◽  
Ion Acoustic ◽  
De Vries ◽  
Ion Collision

AbstractAnalytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the framework of the damped Korteweg–de Vries–Burgers (DKdVB) equation in an unmagnetised collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, q-nonextensive electrons, and neutral particles. Using Reductive Perturbation Technique, the DKdVB equation is obtained for DIAWs. The effects of different physical parameters such as dust ion collision frequency parameter (\({\nu_{id0}}\)), viscosity coefficient (η10), the entropic index (q), the speed of the travelling wave (M0), and the ratio between the unperturbed densities of the electrons and ions (μ) on the analytical solution of DIAWs are observed. The results of the present article may have applications in laboratory and space plasmas.

Analytical Solitary Wave Solution of the Dust Ion Acoustic Waves for the Damped Forced Korteweg–de Vries Equation in Superthermal Plasmas

2018 ◽  
Vol 73 (2) ◽  
pp. 151-159 ◽  
Author(s):  
Prasanta Chatterjee ◽  
Rustam Ali ◽  
Asit Saha
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Perturbation Technique ◽  
Dusty Plasmas ◽  
Periodic Force ◽  
Ion Acoustic ◽  
De Vries ◽  
Dia Waves

AbstractAnalytical solitary wave solution of the dust ion acoustic (DIA) waves was studied in the framework of the damped forced Korteweg–de Vries (DFKdV) equation in superthermal collisional dusty plasmas. The reductive perturbation technique was applied to derive the DKdV equation. It is observed that both the rarefactive and compressive solitary wave solutions are possible for this plasma model. The effects of κ and the strength (f0) and frequency (ω) of the external periodic force were studied on the analytical solitary wave solution of the DIA waves. It is observed that the parameters κ, f0 and ω have significant effects on the structure of the damped forced DIA solitary waves. The results of this study may have relevance in laboratory plasmas as well as in space plasmas.

W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations

2021 ◽  
pp. 2150468
Author(s):  
Youssoufa Saliou ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
M. S. Osman ◽  
Doka Serge Yamigno ◽  
...  
Keyword(s):  
Acoustic Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Singular Function ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Quantum Electron ◽  
Ion Acoustic ◽  
Trigonometric Function Solutions

By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation.

Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950054
Author(s):  
H. Wajahat A. Riaz
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Order Effects ◽  
Darboux Transformations ◽  
De Vries ◽  
Higher Order Effects

Higher-order nonlinear evolution equations are important for describing the wave propagation of second- and higher-order number of fields in optical fiber systems with higher-order effects. One of these equations is the coupled complex modified Korteweg–de Vries (ccmKdV) equation. In this paper, we study noncommutative (nc) generalization of ccmKdV equation. We present Darboux and binary Darboux transformations (DTs) for the nc-ccmKdV equation and then construct its Quasi-Grammian solutions. Further, single and double-hump soliton solutions of first- and second-order are given in commutative settings.

Symbolic Computation and Non-travelling Wave Solutions of the (2+1)-Dimensional Korteweg de Vries Equation

2005 ◽  
Vol 60 (4) ◽  
pp. 221-228 ◽  
Author(s):  
Dengshan Wang ◽  
Hong-Qing Zhang
Keyword(s):  
Symbolic Computation ◽  
Evolution Equations ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
De Vries

Abstract In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2+1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the Jacobi elliptic function, soliton-like trigonometric function solutions, and so on. Our method can be applied to other nonlinear evolution equations.

Nonlinear propagation of dust-acoustic waves in a magnetized dusty plasma with vortex-like ion distribution

1998 ◽  
Vol 59 (3) ◽  
pp. 575-580 ◽  
Author(s):  
A. A. MAMUN
Keyword(s):  
Dusty Plasma ◽  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Nonlinear Propagation ◽  
Charged Dust ◽  
Ion Distribution ◽  
Free Electrons ◽  
Dust Acoustic Waves ◽  
Magnetized Dusty Plasma ◽  
Dust Acoustic

A theoretical investigation has been made of the nonlinear propagation of dust-acoustic waves in a magnetized three-component dusty plasma consisting of a negatively charged dust fluid, free electrons and vortex-like distributed ions. It is found that, owing to the departure from the Boltzmann ion distribution to a vortex-like one, the dynamics of small- but finite-amplitude dust-acoustic waves in a magnetized dusty plasma is governed by the modified Korteweg–de Vries equation. The latter admits a stationary dust-acoustic solitary-wave solution that has larger amplitude, smaller width and higher propagation velocity than that involving adiabatic ions. The effects of external magnetic field, trapped ions and free electrons on the properties of these dust-acoustic solitary waves are briefly discussed.

MODIFIED EXP-FUNCTION METHOD AND VARIABLE-COEFFICIENT KORTEWEG–DE VRIES MODEL FROM BOSE–EINSTEIN CONDENSATES

2010 ◽  
Vol 24 (19) ◽  
pp. 3759-3768 ◽  
Author(s):  
KE-JIE CAI ◽  
CHENG ZHANG ◽  
TAO XU ◽  
HUAN ZHANG ◽  
BO TIAN
Keyword(s):  
Variable Coefficient ◽  
Function Method ◽  
Evolution Equations ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Wave Solutions ◽  
Nonlinear Excitations ◽  
De Vries ◽  
Bose Einstein ◽  
Graphical Illustration

The amplitude of nonlinear excitations in BECs with inhomogeneities is governed by a generalized variable-coefficient Korteweg–de Vries model. With symbolic computation, the Exp-function method is modified to obtain analytical nontraveling solitary-wave and periodic-wave solutions. Through the qualitative analysis and graphical illustration, the inhomogeneous propagation features of solitary waves are discussed, and some observable effects for BEC dynamic in the presence of external potentials are provided. The modified Exp-function method is also applicable to other variable-coefficient nonlinear evolution equations.

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