Integrable dissipative structures in the gauge theory of gravity

Abstract

The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be written as a pair of time reversed evolution equations of the reaction-diffusion type, admitting dissipative solutions. The spectral parameter for the related Lax pair appears as the constant valued spin connection associated with the SO(1, 1) gauge symmetry. Spontaneous breaking of the non-compact symmetry and the irreversible evolution are discussed.

Envelope soliton resonances and broer-kaup-type non-madelung fluids

“…Using the identity ρ x = ρ(log e + ) x + ρ(log e − ) x , we can eliminate one of the velocities and obtain continuity equations for ρ that include only one field e + or e − . Combining with (26) or (27), we then obtain the independent system for e + and ρ,…”

“…At a zero drift velocity, v + (x, t) = 0 or v − (x, t) = 0, this metric develops a horizon singularity and the black-hole-type picture [26]. This metric can be rewritten in terms of the Broer-Kaup hydrodynamics.…”

Резонансы Солитонов Огибающих И Немаделунговы Жидкости Типа Броера - Каупа

“…Для системы РД эта метрика описывает псевдориманову поверхность постоянной скалярной кривизны R = Λ. При нулевой скорости дрейфа v + (x, t) = 0 или v − (x, t) = 0 она порождает сингулярность на горизонте событий и создает картину типа черной дыры [26]. Эту метрику можно записать в терминах гидродинамики БК.…”

The Prolongation Structures for the System of the Reaction-Diffusion Type

“…which has been applied in biological systems, chemical autocatalysis, and also in the gauge formulation of the (1 + 1)-dimensional gravity [3]. Moreover, the geometrical equivalent counterpart of the system (1) is the modified Heisenberg Ferromagnetic (HF) equation [4] [5].…”