Nonlinear theory of large-amplitude stationary solitary waves in symmetric unmagnetized e − e + and C 60 − C 60 + plasmas

Gordienko, V. A.; Dubinova, I. D.; Дубинов, А. Е.

doi:10.1134/s1063780x06110043

Cited by 10 publications

(7 citation statements)

References 7 publications

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“…This work also continues the studies [8][9][10][11][12][13][14][15][16] devoted to the development of the non linear theory of electrostatic waves in ep, eid, and epi plasmas.…”

Section: Introductionmentioning

confidence: 92%

Nonlinear theory of ion-sound waves in a dusty electron-positron-ion plasma

2012

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A theory of ion sound waves in a dusty electron-positron-ion plasma is developed. It is shown in the linear approximation that periodic waves exist in a bounded range of parameters. The expression for the sound velocity is derived and the dependence of the velocity on the space charge of dust particles is analyzed. In the nonlinear theory, the general exact solution is obtained, which is then analyzed using the Bernoulli pseudopotential method. Particular solutions are obtained in the form of nonlinear periodic waves, large amplitude periodic waves (superlinear waves), and solitary compression and rarefaction waves (solitons).

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“…This work also continues the studies [8][9][10][11][12][13][14][15][16] devoted to the development of the non linear theory of electrostatic waves in ep, eid, and epi plasmas.…”

Section: Introductionmentioning

confidence: 92%

Nonlinear theory of ion-sound waves in a dusty electron-positron-ion plasma

2012

Self Cite

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“…The analysis for temperatures to the right of this domain is not as simple. If (14) holds in this region, one of two things may occur. First, if the system is still described by the W −1 branch of the Lambert W function the chemical potential becomes complex.…”

Section: A Chemical Potentialmentioning

confidence: 99%

“…In this case, the fugacity is identically unity and of BEC forms. From (14), for real branches of W , a solution exists iff W j [e −1 (ρλ 4 − (π 2 /6))] → −∞, which is only possible if j = −1 and e −1 ρλ 4 − π 2 6 → 0. Recalling that λ = 2π 2 /(MkT ), we have,…”

Section: A Chemical Potentialmentioning

confidence: 99%

“…In general, (14) allows for the possibility of a complex chemical potential. By choosing j = 0 or j = −1, the chemical potential is real.…”

Section: A Chemical Potentialmentioning

confidence: 99%

“…Therefore, the Lambert W function has the potential to provide solutions to problems that have previously not been solved analytically, as well uncovering novel and interesting properties of previously solved problems. (b) In the field of statistical and plasma physics exponential and logarithmic functions are often encountered 14 and the W function has already proven to be a useful tool. In this work, we will demonstrate some interesting applications of the Lambert W function to D-dimensional Bose gases.…”

Section: Introductionmentioning

confidence: 99%

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D-dimensional Bose gases and the Lambert W function

Tanguay

Gil

Jeffrey

et al. 2010

Journal of Mathematical Physics

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The applications of the Lambert W function (also known as the W function) to D-dimensional Bose gases are presented. We introduce two sets of families of logarithmic transcendental equations that occur frequently in thermodynamics and statistical mechanics and present their solution in terms of the W function. The low temperature T behavior of free ideal Bose gases is considered in three and four dimensions. It is shown that near condensation in four dimensions, the chemical potential μ and pressure P can be expressed in terms of T through the W function. The low T behavior of one-and two-dimensional ideal Bose gases in a harmonic trap is studied. In 1D, the W function is used to express the condensate temperature, T C , in terms of the number of particles N ; in 2D, it is used to express μ in terms of T . In the low T limit of the 1D hard-core and the 3D Bose gas, T can be expressed in terms of P and μ through the W function. Our analysis allows for the possibility to consider μ, T , and P as complex variables. The importance of the underlying logarithmic structure in ideal quantum gases is seen in the polylogarithmic and W function expressions relating thermodynamic variables such as μ, T , and P. C

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On the structure of the solution set of a generalized Euler–Lambert equation

Mező

2017

Journal of Mathematical Analysis and Applications

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Nonlinear theory of large-amplitude stationary solitary waves in symmetric unmagnetized e − e + and C 60 − C 60 + plasmas

Cited by 10 publications

References 7 publications

Nonlinear theory of ion-sound waves in a dusty electron-positron-ion plasma

Nonlinear theory of ion-sound waves in a dusty electron-positron-ion plasma

D-dimensional Bose gases and the Lambert W function

On the structure of the solution set of a generalized Euler–Lambert equation

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