Strongly localized moving discrete dissipative breather-solitons in Kerr nonlinear media supported by intrinsic gain

We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

Moving on from nascent entrepreneurship:measuring cross-national differences in the transition to new business ownership

Nascent entrepreneurship and new business ownership are subsequent stages in the entrepreneurial process. We illustrate how information from the largest internationally harmonized database on entrepreneurship, the Global Entrepreneurship Monitor project, can be used to approximate the entrepreneurial process. We make a methodological contribution by computing the ratio of new business ownership to nascent entrepreneurship in a way that reflects the transition from nascent to new business ownership and provides cross-nationally comparable information on the efficiency of the entrepreneurial process for 48 countries. We report evidence for the validity of the transition ratio by benchmarking it against transition rates obtained from longitudinal studies and by correlating it with commonly used entrepreneurship indicators and macro-level economic indices. The transition ratio enables future cross-national research on the entrepreneurial process by providing a reliable and valid indicator for one key transition in this process. © 2012 Springer Science+Business Media New York.