Journal ArticleDOI
The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations
TLDR
The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived in this paper for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension.Abstract:
The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.read more
Citations
More filters
Journal ArticleDOI
Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations
TL;DR: In this paper, self-similar solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg-deVries equation in one spatial variable were determined by using Lie-group scaling transformation.
Journal ArticleDOI
Hidden symmetries associated with the projective group of nonlinear first-order ordinary differential equations
B Abraham-Shrauner,A Guo +1 more
TL;DR: In this article, Hidden symmetries for non-Abelian, two-parameter subgroups of the projective group have been reported for the Riccati equation and the reaction-diffusion equation.
Journal ArticleDOI
Invariant Linear Spaces and Exact Solutions of Nonlinear Evolution Equations
TL;DR: In this paper, the authors present invariant linear spaces and exact solutions of nonlinear evolution equations in the context of non-linear space and nonlinear nonlinear space, respectively.
Journal ArticleDOI
Symmetry group classification for two-dimensional elastodynamics problems in nonlocal elasticity
TL;DR: In this paper, the symmetry groups of two-dimensional elastodynamics problems in nonlocal elasticity are identified and classified, and the symmetry group classification is determined by using these differential equations and solutions of the determining equations.
Journal ArticleDOI
Lie group analysis of gravity currents
D. Sahin,Nalan Antar,Teoman Özer +2 more
TL;DR: In this paper, the authors investigated the self-similarity solutions of the one-layer shallow-water equations representing gravity currents by using Lie group analysis and it was shown that Lie Group analysis is the generalization of the dimensional analysis for investigating the selfsimilarity solution of the shallow water equations.
References
More filters
Physics of shock waves and high-temperature hydrodynamic phenomena
Ya. B. Zel'dovich,Yu. P. Raizer +1 more
TL;DR: The physics of high-temperature hydrodynamic phenomena is discussed in this article, where the authors present interpretations of the physical basis of shockwave and high temperature hydrodynamics and give practical guidance to those who work with these subjects.
Journal ArticleDOI
Exact Nonlinear Plasma Oscillations
TL;DR: In this paper, it is shown that, by adding appropriate numbers of particles trapped in the potential energy troughs, essentially arbitrary traveling wave solutions can be constructed, and the possible existence of such waves in an actual plasma will depend on factors ignored in this paper, as in most previous works, namely interparticle collisions and the stability of the solutions against various types of perturbations.
Book
Similarity methods for differential equations
George W. Bluman,Julian D. Cole +1 more
TL;DR: In this paper, the authors define the notion of groups of transformations and prove that a one-parameter group essentially contains only one infinitesimal transformation and is determined by it.
Journal ArticleDOI
A direct approach to finding exact invariants for one‐dimensional time‐dependent classical Hamiltonians
H. Ralph Lewis,P. G. L. Leach +1 more
TL;DR: For a classical Hamiltonian H=(1/2)p2+V(q,t) with an arbitrary time-dependent potential V(qs,t), exact invariants that can be expressed as series in positive powers of ǫ p, I(qp,p,t)=∑∞n=0pnfn(qs),t, are examined in this article.