New classes of similarity solutions for the nonlinear Carleman-Boltzmann equation

DOI10.1016/0378-4371(86)90110-XzbMath0669.58046OpenAlexW2012842512MaRDI QIDQ1118889

G. Dukek, Theo F. Nonnenmacher

Publication date: 1986

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(86)90110-x

zbMATH Keywords

Carleman-modelLie-group based similarity method

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Applications of global analysis to the sciences (58Z05) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items

On group invariant solutions of the Boltzmann equation ⋮ Similarity analysis and exact solutions for a general discrete two- velocity model of Boltzmann equation ⋮ Lie group analysis for a multispecies, spatially inhomogeneous, mutually interacting gas mixture ⋮ Solutions to the nonlinear Boltzmann equation for particle transport in a host medium ⋮ Similarity solutions in space dependent extended kinetic theory ⋮ New classes of similarity solutions for the nonlinear Carleman-Boltzmann equation ⋮ Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential ⋮ Exact solutions in 1+1 dimensions of the general two-velocity discrete Illner model

Cites Work

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• Similarity methods for differential equations
• Propagation of singularities for non-linear wave equations in one dimension
• Two classes of explicit solutions of the carleman model
• An exponential formula for solving Boltzmann's equation for a Maxwellian gas