Differential equations, especially nonlinear, present the most effective way for describing
complex physical processes. Methods for constructing exact solutions of differential …

This paper is devoted to a personal overview about weak symmetries of partial differential
equations. The relationship between weak symmetries and overdetermined systems of …

In this paper, based on differential characteristic set theory and the associated algorithm
(also called Wuʼs method), an algorithmic method is presented to decide on the existence …

We study the steady two-dimensional boundary-layer equations in the flat and axisymmetric
case to show that some similarity reductions already found in the literature with ad hoc new …

We describe an adaption of a differential algebraic completion algorithm for linear systems
of partial differential equations that allows us to deduce intrinsic differential geometric …

We consider general systems of ordinary and partial differential equations from a geometric
point of view. This leads to simple interpretations of various index concepts introduced for …

An involution refers to a function that acts as its own inverse. In this paper, our focus lies on
exploring two-dimensional involutive maps defined by rational functions. These functions …

We present an informal overview of a number of approaches to di erential equations which
are popular in computer algebra. This includes symmetry and completion theory, local …

We investigate a general approach for solving a partial differential equation by using the
differential invariants of its point symmetries. By first solving its quotient PDE, which is given …

We present an overview of the MuPAD library DETools for the analysis of differential
equations. It has been developed within an object-oriented environment for the efficient …