Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied
mathematics and algebra, this book presents an innovative synthesis of methods used to …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

In this paper we discuss symmetry reductions and exact solutions of the Boussinesq
equation using the classical Lie method of infinitesimals, the direct method due to Clarkson …

We consider classes C of differential equations characterized by the presence of arbitrary
elements, that is, arbitrary functions or constants. Based on an idea of Ovsiannikov, we …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

We first show that the infinitesimal generator of Lie symmetry of a time-fractional partial
differential equation (PDE) takes a unified and simple form, and then separate the Lie …

The invariant analysis of time-fractional nonlinear differential-difference equations and
determination of their exact solutions using the Lie symmetry method is not discussed in the …

Binary symmetry constraints of the 𝒩-wave interaction equations in 1+ 1 and 2+ 1
dimensions are proposed to reduce the 𝒩-wave interaction equations into finite-dimensional …

There are symbolic programs based on heuristics that sometimes, but not always, explicitly
integrate the determining equations for the infinitesimal Lie symmetries admitted by systems …

An algorithm is presented to linearize nonlinear partial differential equations by non-
invertible mappings. The algorithm depends on finding nonlocal symmetries of the given …