This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.

We compare two approaches to Semi-Riemannian metrics of low regularity. The maximally “reasonable” distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombeau.

The axiomatic formulation of quantum field theory (QFT) of the 1950’s in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the construction of a wealth of (2dimensional) soluble QFT models with quadratic exchange relations, and, on the mathematical side, the introduction of the Colombeau...

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new notions of ellipticity and hypoellipticity, study their interrelation, and give a number of new examples and counterexamples. Using the concept of G∞-regularity of...