5 research outputs found
Hawking-like emission in kink-soliton escape from a potential well.
The escape of solitons over a potential barrier is analysed within the framework of a nonlinear Klein–Gordon equation. It is shown that the creation of a kink–antikink pair near the barrier through an internal mode instability can be followed by escape of the kink in a process analogous to Hawking radiation. These results have important implications in a wider context, including stochastic resonance and ratchet systems, which are also discussed
Universal functions and exactly solvable chaotic systems
A universal differential equation is a nontrivial differential equation the
solutions of which approximate to arbitrary accuracy any continuous function on
any interval of the real line. On the other hand, there has been much interest
in exactly solvable chaotic maps. An important problem is to generalize these
results to continuous systems.
Theoretical analysis would allow us to prove theorems about these systems and
predict new phenomena. In the present paper we discuss the concept of universal
functions and their relevance to the theory of universal differential
equations. We present a connection between universal functions and solutions to
chaotic systems. We will show the statistical independence between and
(when is not equal to zero) and is a solution to
some chaotic systems. We will construct universal functions that behave as
delta-correlated noise. We will construct universal dynamical systems with
truly noisy solutions. We will discuss physically realizable dynamical systems
with universal-like properties.Comment: 12 Pages, 9 figures. Proceedings 1st Meeting IST-IM