A sizable literature exists on discrete quantum mechanics, that is on quantum mechanics in
discrete space–time. We refer to a recent review for motivation and for an extensive list of …

The group classification problem for the class of (1+ 1)-dimensional linear rth order evolution
equations is solved for arbitrary values of r> 2. It is shown that a related maximally gauged …

We completely solve the equivalence problem for Euler–Bernoulli equation using Lie
symmetry analysis. We show that the quotient of the symmetry Lie algebra of the Bernoulli …

The governing equations for plane stress deformations of isotropic incompressible
hyperelastic materials are highly nonlinear and consequently very few exact solutions are …

The determining equations for the nonclassical reductions of the heat and Burgers'
equations are considered. It is shown that both systems belong to a Burgers' equation …

Computing the Lie point symmetries of systems of linear differential equations can be
prohibitively difficult. For homogeneous systems in Kovalevskaya form of order two or …

In this paper, we show that for a class of nonlinear partial differential equations with arbitrary
order the determining equations for the nonclassical reduction can be obtained by requiring …

A form of the solute transport equation is transformed from Cartesian to streamline
coordinates. Symmetry analysis of this equation with a point water source reveals a 5 …

It is generally known that classical point and potential Lie symmetries of differential
equations (the latter calculated as point symmetries of an equivalent system) can be …

A class of nonlinear Galilei-invariant generalizations of the heat equation admitting infinite-
dimensional Lie symmetry is presented. Lie symmetries and examples of exact solutions are …