arXiv subjects

Piotr Goldstein

Publications and source records attributed to Piotr Goldstein.

3 recordsLinked to original sources

arXiv2022

Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario

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 solutions in the Painlevé sense. We prove that they are unstable in the vicinity of the cosmological singularity. Regularity of the dynamics is also examined with the dynamical systems method. Our results confirm the conjecture of BKL that the dynamics near the singularity becomes generically chaotic.

gr-qc↗

arXiv2016

Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas

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 stability. Known soliton results are recovered as special cases. A historical overview of the problem concludes the paper.

nlin.PS↗

arXiv1995

Isothermic surfaces in $\E^3$ as soliton surfaces

We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton) systems. This enables one to study the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral methods available in the soliton theory. Also the associated non-linear system is interesting in itself since it displays some unconventional soliton features and, physically, could be applied in the theory of infinitesimal deformations of membranes.

solv-int↗