Maria Paola Speciale

Similarity reduction and closed form solutions for a model derived from two-layer fluids

In this paper, we study an integrable system of coupled KdV equations, derived by Gear and Grimshaw (Stud. Appl. Math. 70(3):235-258, 1984), modeling the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. In particular, we present the complete group classification of the model and find conditions on arbitrary parameters for which the system admits symmetries. Some exact solutions of physical relevance are derived.

Exact solutions to the equations of ideal gas-dynamics by means of the substitution principle

Abstract In this paper the equations governing three-dimensional unsteady flows of an inviscid, thermally non-conducting fluid, subjected to no extraneous force, are considered. First, some simple exact solutions are explicitly determined; then, by using the invariance of the given equations with respect to a generalized stretching group of all but space variables and a generalized time translation new solutions are immediately constructed. This invariance is known in the literature as substitution principle, since it allows to generate new solutions (substituted flows) from given solutions.

Conservation laws for a model derived from two layer-fluids

In this paper, using a recent approach for finding conservation laws, based on Lie symmetries, we establish the conservation laws for a model admitting quasi self-adjoint equations.

New exact solutions for a coupled KdV-like model

An extension of a recent method is applied in order to construct new explicit exact solutions for a system of coupled KdV-like equations.

On a hierarchy of traveling wave solutions in a shallow stratified fluid

An algebraic method is applied to construct a complete hierarchy of traveling wave solutions for a system of coupled KdV-like equations.

Analytical and numerical solutions of fractional type advection-diffusion equation

In this paper, the case of an equation involving fractional derivatives with respect to a single independent variable has been analyzed. Our aim is to determine its Lie’s symmetry, and by using them, obtain analytical and numerical solutions.

Wave hierarchies in continua with scalar microstructure in the plane and spherical symmetry

In this paper, we consider the balance equations for a continuum with scalar microstructure and propose a general approach to investigate nonlinear wave propagation by means of an asymptotic approach within the theoretical context of wave hierarchies. The evolution equations that are obtained for the leading terms of the asymptotics allow for the description of various levels of wave motion in agreement with the different scales involved in the modelling of continua with microstructure. Both the one-dimensional planar and the axisymmetric spherical cases are considered in a unified way, and various examples (immiscible mixtures of perfect fluids, granular materials, liquid with bubbles) are discussed in order to illustrate the procedure.