scholarly journals Reductive Perturbation Approach to Chemical Instabilities

1974 ◽  
Vol 52 (4) ◽  
pp. 1399-1401 ◽  
Author(s):  
Y. Kuramoto ◽  
T. Tsuzuki
Keyword(s):  
Perturbation Approach ◽  
Reductive Perturbation ◽  
Chemical Instabilities

scholarly journals Reductive Perturbation Approach to the Fluctuation

1975 ◽  
Vol 54 (2) ◽  
pp. 585-587 ◽  
Author(s):  
A. Ito ◽  
T. Ohta ◽  
H. Mashiyama
Keyword(s):  
Perturbation Approach ◽  
Reductive Perturbation

scholarly journals Modified Korteweg–de Vries solitons at supercritical densities in two-electron temperature plasmas

2016 ◽  
Vol 82 (2) ◽  
Author(s):  
Frank Verheest ◽  
Carel P. Olivier ◽  
Willy A. Hereman
Keyword(s):  
Soliton Solutions ◽  
Detailed Comparison ◽  
Mkdv Equation ◽  
Perturbation Approach ◽  
Electron Population ◽  
Positive Ions ◽  
Reductive Perturbation ◽  
De Vries ◽  
Temperature Electron ◽  
Two Temperature

The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg–de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obtained from the more complete Sagdeev solution and that only slightly superacoustic mKdV solitons have acceptable amplitudes and widths, in the light of the full solutions.

scholarly journals On the Effect of Electron Streaming and Existence of Quasi-Solitary Mode in a Strongly Coupled Quantum Dusty Plasma—Far and Near Critical Nonlinearity

Plasma ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 408-425
Author(s):  
Shatadru Chaudhuri ◽  
Asesh Roy Chowdhury
Keyword(s):  
Dusty Plasma ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Elliptic Functions ◽  
Mkdv Equation ◽  
Perturbation Approach ◽  
Strongly Coupled ◽  
Critical Situation ◽  
The Kdv Equation ◽  
Reductive Perturbation

As strongly coupled quantum dusty plasma consisting of electrons and dust with the ions in the background is considered when there is a streaming of electrons. It is observed that the streaming gives rise to both the slow and fast modes of propagation. The nonlinear mode is then analyzed by the reductive perturbation approach, resulting in the KdV-equation. In the critical situation where non-linearity vanishes, the modified scaling results in the MKdV equation. It is observed that both the KdV and MKdV equations possess quasi-solitary wave solution, which not only has the character of a soliton but also has a periodic nature. Such type of solitons are nowadays called nanopteron solitons and are expressed in terms of cnoidal-type elliptic functions.

scholarly journals A Reductive Perturbation Approach to Hard-Mode Instabilities of Inverted-Type Bifurcations

1981 ◽  
Vol 66 (1) ◽  
pp. 143-153 ◽  
Author(s):  
K. Yamafuji ◽  
K. Toko ◽  
J. Nitta ◽  
K. Urahama
Keyword(s):  
Perturbation Approach ◽  
Reductive Perturbation
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