This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an +xn+1)/xn, where {an} is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k ∈ {1, 2, 3, 6} the behavior of the sequence {xn} is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases ...

in this paper we obtain  exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    the methods used  to determine the exact solutions of the underlying equation are the lie group analysis  and the simplest equation method. the solutions obtained are  then plotted.

The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles Ai (i = 1, . . . , 8) with different masses. The heaviest five lie above threshold and owe their stability to integrability. We use form factor perturbation theory to compute the decay widths of the first two particles above threshold when integrability is broke...

Several recently developed techniques for reconstructing surface shape from shading information estimate surface slopes without ensuring that they a re integrable. This paper presents a n approach for enforcing integrability, a particular implementation of the approach, a n example of its application to extending a n existing shapefrom-shading algorithm, and experimental results showing the imp...

where all but one “masses” are equal, m1 = m −1, m2 = . . . = mn = 1, m is a real parameter, p̂j = i ∂ ∂xj , j = 1, . . . , n, and ℘ is the classical Weierstrass elliptic function. The case when m is integer is a special one: in that case a stronger version of integrability (the so-called algebraic integrability) was conjectured [2]. The first results in this direction were found in [3], where i...

We apply the Painlevé test for integrability to the new discrete nonlinear Schrödinger equation introduced by Leon and Manna. Since the singular expansions of solutions of this equation turn out to contain non-dominant logarithmic terms, we conclude that the studied equation is nonintegrable. This result supports the recent observation of Levi and Yamilov that the Leon–Manna equation does not a...

In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value are al...