Dispersion relation of the non-linear Klein-Gordon equation through a variational method

We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the Linear Delta Expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of accuracy. We compare our findings with similar results in the literature and show that our approach leads to better and simpler results.Comment: 10 pages, 3 figures, matches published versio

PUBLIC INVESTMENT IN TRANSPORTATION INFRASTRUCTURES AND INDUSTRY PERFORMANCE IN PORTUGAL

The objective of this paper is to evaluate the effects at the industry level of public investment in transportation infrastructures in Portugal. The empirical results are based on VAR/ECM models for the Portuguese economy and for eighteen industries covering the whole spectrum of economic activity in the country. These models consider private-sector output, employment and investment as well as public investment. Empirical results at the aggregate level indicate that public investment has a positive effect on both private inputs as well as on private output and that it affects labor productivity positively. These aggregate results, however, hide a wide variety of industry-level effects. In absolute terms, the industries that benefit the most from public investment are Construction, Trade, Transportation, Finance, Real Estate, and Services. In turn, relative to their size, the industries that benefit the most are Mining, Non-Metal Products, Metal Products, Construction, Restaurants, Transportation, and Finance, and, therefore, public investment tends to shift the industry mix toward these industries. Accordingly, our empirical results suggest that although public investment has been a powerful instrument to enhance the long-term economic performance in Portugal it does so in a way that is rather unbalanced across industries.Infrastructures, Industry Performance, Portugal