99 citations · 151 across the 11 of their papers we have counts for
11 papers
Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario
Piotr Goldstein, Włodzimierz Piechocki
A class of exact solutions to the Belinski-Khalatnikov-Lifshitz (BKL) scenario is derived and tested for their stability against small perturbations. These are the only regular sol…
The spin representations via sigma models
P. P. Goldstein, A. M. Grundland, A. M. Escobar Ruiz
We establish and analyze a new relationship between the matrices describing an arbitrary component of a spin , where , and the matrices of …
On extending the Painlevé test to the one-dimensional Vlasov equation
Piotr P. Goldstein
An analysis of possible extension of the Painlevé test, to encompass the one-dimensional Vlasov equation, is performed. The extending requires a nontrivial generalization of the te…
The Painlevé property of sigma models
P P Goldstein, A M Grundland
We test the sigma models for the Painlevé property. While the construction of finite action solutions ensures their meromorphicity, the general case requires te…
On a stack of surfaces obtained from the sigma models
P P Goldstein, A M Grundland
Under the assumption that the sigma model is defined on the Riemann sphere and its action functional is finite, we derive surfaces induced by surfaces and we de…
Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas
Piotr Goldstein, Eryk Infeld
Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for st…