Group Analysis of the One-Dimensional Boltzmann Equation: IV. Complete Group Classification in the General Case

Theoretical and Mathematical Physics ◽

10.1134/s0040577919110072 ◽

2019 ◽

Vol 201 (2) ◽

pp. 1614-1643 ◽

Author(s):

A. V. Borovskikh ◽

K. S. Platonova

Keyword(s):

Boltzmann Equation ◽

Group Analysis ◽

Group Classification ◽

Complete Group ◽

One Dimensional ◽

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Group analysis of the one-dimensional Boltzmann equation. Invariants and the problem of moment system closure

Theoretical and Mathematical Physics ◽

10.1134/s0040577921090014 ◽

2021 ◽

Vol 208 (3) ◽

pp. 1165-1181

Author(s):

K. S. Platonova ◽

A. V. Borovskih

Keyword(s):

Boltzmann Equation ◽

Group Analysis ◽

One Dimensional ◽

Moment System ◽

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Group analysis of the one-dimensional Boltzmann equation: I. symmetry groups

Differential Equations ◽

10.1134/s0012266117040115 ◽

2017 ◽

Vol 53 (4) ◽

pp. 530-538 ◽

Author(s):

K. S. Platonova

Keyword(s):

Boltzmann Equation ◽

Group Analysis ◽

Symmetry Groups ◽

One Dimensional ◽

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Group analysis of the one-dimensional boltzmann equation: II. Equivalence groups and symmetry groups in the special case

Differential Equations ◽

10.1134/s0012266117060106 ◽

2017 ◽

Vol 53 (6) ◽

pp. 796-808 ◽

Author(s):

K. S. Platonova

Keyword(s):

Boltzmann Equation ◽

Group Analysis ◽

Symmetry Groups ◽

One Dimensional ◽

The One ◽

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Group Analysis of the One-Dimensional Boltzmann Equation: III. Condition for the Moment Quantities to Be Physically Meaningful

Theoretical and Mathematical Physics ◽

10.1134/s0040577918060077 ◽

2018 ◽

Vol 195 (3) ◽

pp. 886-915 ◽

Author(s):

K. S. Platonova ◽

A. V. Borovskikh

Keyword(s):

Boltzmann Equation ◽

Group Analysis ◽

One Dimensional ◽

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On the complete group classification of the one-dimensional nonlinear Klein-Gordon equation with a delay

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.3769 ◽

2015 ◽

Vol 39 (12) ◽

pp. 3255-3270 ◽

Author(s):

Feng-Shan Long ◽

S. V. Meleshko

Keyword(s):

Gordon Equation ◽

Group Classification ◽

Complete Group ◽

One Dimensional ◽

Klein Gordon ◽

The One ◽

Klein Gordon Equation

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Group analysis of the one dimensional wave equation with delay

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125193 ◽

2020 ◽

Vol 378 ◽

pp. 125193 ◽

Author(s):

Jervin Zen Lobo ◽

Y.S. Valaulikar

Keyword(s):

Wave Equation ◽

Group Analysis ◽

One Dimensional ◽

The One ◽

Equation With Delay ◽

Dimensional Wave

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A solution of the one-dimensional linear quartic Poisson-Boltzmann equation using lattice-Boltzmann

Contemporary Engineering Sciences ◽

10.12988/ces.2018.84163 ◽

2018 ◽

Vol 11 (33) ◽

pp. 1613-1619

Author(s):

F. Fonseca

Keyword(s):

Boltzmann Equation ◽

Lattice Boltzmann ◽

One Dimensional ◽

Poisson Boltzmann ◽

Poisson Boltzmann Equation ◽

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Renormalization group analysis of the one-dimensional extended Hubbard model

Physical Review B ◽

10.1103/physrevb.83.075111 ◽

2011 ◽

Vol 83 (7) ◽

Author(s):

M. Ménard ◽

C. Bourbonnais

Keyword(s):

Renormalization Group ◽

Hubbard Model ◽

Group Analysis ◽

Extended Hubbard Model ◽

Renormalization Group Analysis ◽

One Dimensional ◽

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Symmetries and invariant solutions of the one-dimensional Boltzmann equation for inelastic collisions

Theoretical and Mathematical Physics ◽

10.1134/s0040577916020045 ◽

2016 ◽

Vol 186 (2) ◽

pp. 183-191 ◽

Author(s):

O. V. Ilyin

Keyword(s):

Boltzmann Equation ◽

Inelastic Collisions ◽

Invariant Solutions ◽

One Dimensional ◽

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Explicit expression for the fundamental solution to the Cauchy problem for the one-velocity Boltzmann equation in the case of a one-dimensional isotropic medium

Journal of Mathematical Sciences ◽

10.1007/bf02365051 ◽

1999 ◽

Vol 97 (4) ◽

pp. 4368-4389

Author(s):

Yu. B. Yanushanets

Keyword(s):

Cauchy Problem ◽

Boltzmann Equation ◽

Fundamental Solution ◽

Explicit Expression ◽

Isotropic Medium ◽

One Dimensional ◽

The Cauchy Problem ◽

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