N. Manganaro

TL;DR: In this article, generalized simple wave solutions to quasilinear hyperbolic nonhomogeneous systems of PDEs were obtained through the differential constraint method, which proved to be flexible enough to solve generalized Riemann problems where discontinuous initial data are involved.

TL;DR: Within the theoretical framework of differential constraints method, a nonhomogeneous model describing traffic flows is considered in this paper, where classes of exact solutions to the governing equations under interest are determined, and generalized Riemann problems which model situations of interest for traffic flows are solved.

TL;DR: Differential constraints are used as a means of developing a systematic method for finding exact solutions to quasilinear nonautonomous hyperbolic systems of first-order partial differential equations (PDEs) involving two independent variables as mentioned in this paper.

TL;DR: In this paper, the authors categorize classes of coupled nonlinear Schrodinger equations which allow generalized similarity solutions, using the approach of Clarkson and Kruskal (1989), and show that the resulting pair of ordinary differential equations belong to a single class.

TL;DR: In this article, a reduction approach is used to determine solutions in a closed form to the highly nonlinear hodograph system arising from 2 × 2 hyperbolic nonhomogeneous models.