The theory of nonlinear ion-acoustic waves revisited

1996 ◽  
Vol 56 (3) ◽  
pp. 441-450 ◽  
Author(s):  
W. Malfliet ◽  
E. Wieërs
Keyword(s):  
Acoustic Waves ◽  
Collisionless Plasma ◽  
Travelling Wave ◽  
Perturbation Approach ◽  
Third Order ◽  
Ion Acoustic Waves ◽  
First Order ◽  
Basic Set ◽  
Ion Acoustic ◽  
Higher Order Corrections

The basic set of equations describing nonlinear ion-acoustic waves in a cold collisionless plasma, in the limit of long wavelengths, is reconsidered. First, a travelling-wave solution is found up to third order by means of a straightforward perturbation approach based on the smallness of the wavenumber. As a result, a positive dressed solitary wave shows up, which is larger, taller and faster than the KdV soliton, the first-order result. Furthermore, the accuracy of this approach is tested and compared with previous result. Secondly, the reductive perturbation techique to study higher-order corrections is revised and adapted to the present problem.

Bifurcation Analysis for Small-Amplitude Nonlinear and Supernonlinear Ion-Acoustic Waves in a Superthermal Plasma

2020 ◽  
Vol 75 (3) ◽  
pp. 183-191 ◽  
Author(s):  
Durga Prasad Chapagai ◽  
Jharna Tamang ◽  
Asit Saha
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Acoustic Waves ◽  
Small Amplitude ◽  
Perturbation Technique ◽  
Travelling Wave ◽  
Mkdv Equation ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Superthermal Plasma

AbstractBifurcation analysis of small-amplitude nonlinear and supernonlinear periodic ion-acoustic waves (SNPIAWs) is reported in a three-constituent superthermal plasma composing of cold fluid ions and kappa-distributed electrons of two temperatures (cold and hot). Using the reductive perturbation technique, the plasma system is studied under the Korteweg-de Vries (KdV) and the modified KdV (mKdV) equations. Furthermore, the KdV and mKdV equations are transformed into planar dynamical systems applying travelling wave transfiguration. Possible qualitative phase profiles for the corresponding dynamical systems controlled by system parameters ($\kappa,{\alpha_{c}},{\alpha_{h}}$ and f) are shown. Small-amplitude SNPIAW solution for the mKdV equation is presented for the first time. Small-amplitude nonlinear periodic ion-acoustic wave (NPIAW) and ion-acoustic solitary wave solutions (IASWS) for both the KdV and mKdV equations are obtained. Effects of parameters κ and αh on IASW, NPIAW and SNPIAW solutions are investigated.

Propagation of ion acoustic waves in a warm multicomponent plasma with an electron beam

1999 ◽  
Vol 61 (2) ◽  
pp. 177-189 ◽  
Author(s):  
W. M. MOSLEM
Keyword(s):  
Electron Beam ◽  
Evolution Equation ◽  
Acoustic Waves ◽  
Reductive Perturbation Method ◽  
Negative Ion ◽  
Ion Acoustic Waves ◽  
Ion Density ◽  
Basic Set ◽  
Ion Acoustic ◽  
Small Wave

The nonlinear wave structures of small-amplitude ion acoustic waves in a warm plasma with adiabatic negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures) in the vicinity of the critical negative-ion density are investigated using reductive perturbation method. The basic set of equations is reduced to an evolution equation that includes quadratic and cubic nonlinearities. The effective potential of this equation agrees exactly, for small wave amplitudes, with the Sagdeev potential obtained from the original fluid equations using a pseudopotential method. This implies that the evolution equation holds not only in the vicinity of the critical negative-ion density but also in the whole range of negative-ion density under the condition of small wave amplitude.

Multistability and chaotic scenario in a quantum pair-ion plasma

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Barsha Pradhan ◽  
Sayan Mukherjee ◽  
Asit Saha ◽  
Hayder Natiq ◽  
Santo Banerjee
Keyword(s):  
Lyapunov Exponents ◽  
Acoustic Waves ◽  
Negative Ions ◽  
Travelling Wave ◽  
Basins Of Attraction ◽  
Quantum Plasma ◽  
Ion Acoustic Waves ◽  
Ion Acoustic ◽  
Arbitrary Amplitude ◽  
Basic Equations

AbstractMultistability and chaotic scenario of arbitrary amplitude ion-acoustic waves in a quantum plasma consisting of negative ions, positive ions and electrons are investigated. The normalized basic equations are transformed to a four dimensional conservative dynamical system by introducing a travelling wave variable. Stability of the fixed points for the corresponding linearized system is briefly examined. Chaotic and quasi-periodic features of the arbitrary amplitude ion-acoustic waves are discussed using effective tools, viz. phase orientations, time series graph and graphs of Lyapunov exponents. Multistability phenomena is established with the help of phase spaces, largest Lyapunov exponents and cross-section of basins of attraction. The chaotic phenomena is further verified by 0−1 test. Results of this study can be applied in understanding dynamical phenomena of arbitrary amplitude ion-acoustic waves in quantum pair-ion plasmas.

Higher order contributions to ion acoustic solitary waves in a plasma consisting of warm ions and nonisothermal electrons

1982 ◽  
Vol 60 (4) ◽  
pp. 392-396 ◽  
Author(s):  
M. K. Kalita ◽  
S. Bujarbarua
Keyword(s):  
Acoustic Waves ◽  
Solitary Wave Solution ◽  
Reductive Perturbation Method ◽  
Electron Velocity ◽  
Nonlinear Propagation ◽  
Third Order ◽  
Ion Acoustic Waves ◽  
Electron Velocity Distribution ◽  
The Third ◽  
Ion Acoustic

Considering the electron velocity distribution far from Maxwellian, we have investigated the nonlinear propagation of ion acoustic waves in a plasma consisting of warm ions. The solitary wave solution has been obtained for this case retaining terms up to the third order in the usual reductive perturbation method.

scholarly journals Modulation Instability of Ion-Acoustic Waves in Plasma with Nonthermal Electrons

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Basudev Ghosh ◽  
Sreyasi Banerjee
Keyword(s):  
Acoustic Waves ◽  
Modulational Instability ◽  
Perturbation Technique ◽  
Collisionless Plasma ◽  
Multiple Scale ◽  
Ion Temperature ◽  
Nls Equation ◽  
Ion Acoustic Waves ◽  
Nonthermal Electrons ◽  
Ion Acoustic

Modulational instability of ion-acoustic waves has been theoretically investigated in an unmagnetized collisionless plasma with nonthermal electrons, Boltzmann positrons, and warm positive ions. To describe the nonlinear evolution of the wave amplitude a nonlinear Schrödinger (NLS) equation has been derived by using multiple scale perturbation technique. The nonthermal parameter, positron concentration, and ion temperature are shown to play significant role in the modulational instability of ion-acoustic waves and the formation of envelope solitons.

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