New Horizons in Mathematical Physics

5

Authors: Peter K F Kuhfittig

This paper presents a new wormhole solution by assuming that a homogeneously distributed fluid with equation of state p = ωρ can be adapted to an anisotropic spacetime such as a wormhole and that this spacetime admits a one-parameter group of conformal motions. The pressure p in the equation of state becomes the lateral pressure pt instead of the radial pressure pr, as assumed in previous studies. Given that pt = ωρ, pr is then determined from the Einstein field equations. A wormhole solution can be obtained only if ω < −1 or 0 < ω < 1. Since the former case corresponds to phantom dark energy, which has been the subject of earlier studies, we concentrate mainly on the latter. This case implies that given the above conditions, dark matter can support traversable wormholes.

7

Authors: P. Gaillard

In this paper, we go on with the study of rational solutions to the Kadomtsev-Petviashvili equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials of degree 60 in x, y and t depending on 8 parameters. The maximum modulus of these solutions at order 5 is checked as equal to 2(2N + 1)2 = 242. We study their modulus patterns in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, a4, b1, b2, b3, b4. We get triangle and ring structures as obtained in the case of the NLS equation.