Analytical Solution of the Nonlinear Boltzmann Equation For Multicomponent Systems
Abstract
We present exact analytical solutions to the nonlinear relativistic Boltzmann equation for homogeneous, isotropic massless multi-component systems with non-isotropic scattering cross sections. For a two-component system, we identify three distinct classes of exact solutions, each corresponding to specific constraints among initial energy densities, particle number densities, and scattering cross sections. These solutions comprise the equilibrium state and two novel classes: a hybrid structure featuring a non-equilibrium Maxwell-Juttner distribution coupled with a nontrivial distribution; the former is unprecedented in kinetic theory, while the latter refers to nontrivial dynamics shared by both species, which is novel in the relativistic context.
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BibTeX
@misc{wei2026analytical,
title = {{Analytical Solution of the Nonlinear Boltzmann Equation For Multicomponent Systems}},
author = {Linyuan Wei and Yi Wang and Jin Hu and Baoyi Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26845},
eprint = {2609.26845},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26845},
note = {CC0},
}
RIS
TY - UNPB
TI - Analytical Solution of the Nonlinear Boltzmann Equation For Multicomponent Systems
AU - Linyuan Wei
AU - Yi Wang
AU - Jin Hu
AU - Baoyi Chen
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26845
UR - https://arxiv.org/abs/2609.26845
AB - We present exact analytical solutions to the nonlinear relativistic Boltzmann equation for homogeneous, isotropic massless multi-component systems with non-isotropic scattering cross sections. For a two-component system, we identify three distinct classes of exact solutions, each corresponding to specific constraints among initial energy densities, particle number densities, and scattering cross sections. These solutions comprise the equilibrium state and two novel classes: a hybrid structure featuring a non-equilibrium Maxwell-Juttner distribution coupled with a nontrivial distribution; the former is unprecedented in kinetic theory, while the latter refers to nontrivial dynamics shared by both species, which is novel in the relativistic context.
ER -