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From Vlasov–Poisson to Korteweg–de Vries and Zakharov–Kuznetsov
- Source :
- Communications in Mathematical Physics. 324:961-993
- Publication Year :
- 2013
- Publisher :
- Springer Science and Business Media LLC, 2013.
-
Abstract
- We introduce a long wave scaling for the Vlasov-Poisson equation and derive, in the cold ions limit, the Korteweg-De Vries equation (in 1D) and the Zakharov-Kuznetsov equation (in higher dimensions, in the presence of an external magnetic field). The proofs are based on the relative entropy method.
- Subjects :
- Kullback–Leibler divergence
Mathematics::Analysis of PDEs
Complex system
FOS: Physical sciences
Poisson distribution
01 natural sciences
symbols.namesake
Mathematics - Analysis of PDEs
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Physics::Plasma Physics
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Limit (mathematics)
0101 mathematics
Scaling
Mathematical Physics
Mathematical physics
Vries equation
Physics
010102 general mathematics
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Magnetic field
010101 applied mathematics
Nonlinear Sciences::Exactly Solvable and Integrable Systems
symbols
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 14320916 and 00103616
- Volume :
- 324
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....c2f73621dd53822dc7c113bd38f87c4b
- Full Text :
- https://doi.org/10.1007/s00220-013-1825-8