# Staff Directory

## Ronald Wiltshire

#### Contact Details

- Emeritus Professors
- Emeritus Professor
- ron.wiltshire@southwales.ac.uk

## Qualifications

BSc (Hons), PhD, FInstP, CPhys

## About

## Responsibilities

**Main Teaching Areas:**

Partial Differential equations

Non-linear mathematics

Service mathematics

## Publications

**Selected Publications:**

RJ Wiltshire 2006 Isotropy, shear, symmetry and exact solutions for relativistic fluid spheres. Class. Quant. Grav. To appear.

RJ Wiltshire, 2006 Two approaches to the calculation of approximate symmetries exemplified using a system of advection diffusion equations. Journ. Comp.and App. Math. To appear

RJ Wiltshire & C. Sophocleous 2005 An application of the Weiss algorithm of Painleve analysis to create solutions of the reaction diffusion equation. The 10th International Conference in Modern Group Analysis. In Group Analysis of Differential Equations. Ed NH Ibragimov, C. Sophocleous, PA Damianou

RJ Wiltshire & PH Messenger. 2004 Slowly, rotating, compact fluid sources embedded in Kerr empty space-time. Gen. Rel. & Grav. 36 1417-1433.

RJ Wiltshire & PH Messenger, 2003 Robertson-Walker Fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter. Gen. Rel. & Grav. 35 1417-1433.

RJ Wiltshire, 2003 Slowly Rotating, Non-stationary fluid solutions of Einstein’s equations and their match to Kerr space-time. Gen Rel & Grav. 35, 175-187.

RJ Wiltshire & M El-Kafri. 2003 Non-classical and potential symmetry analysis of Richardâ€™s equation for moisture flow in soil. J. Phys A Math. Gen. 37 3 823-839

A Nikitin & RJ Wiltshire. 2001 Systems of Reaction Diffusion Equations and their Symmetry Properties. J. Maths. Phys. 42, 4, 1666-1688

V. Baikov,A. Gladkov and RJ Wiltshire. 1999 Systems of Non-linear Diffusion Equations: A Lie Symmetry Analysis.. Modern Group Analysis VII Ed. NH Ibragimov, K Razi Naqui, E. Straume. MARS Publishers. 9-16 .

AP Belov, JD Giles and RJ Wiltshire. 1999 Analysis of a model of buoyant cyanobacteria population growth. IMA J. Maths. App. in Medicine & Biology. 16. 93-110.

VA Baikov, AV Gladkov, RJ Wiltshire 1998 Lie symmetry classification analysis for nonlinear coupled diffusion..J. Phys A: Math. Gen. 31,7483-7499.

R Shepherd, RJ Wiltshire Spectral decompositions in nonlinear coupled diffusion. IMA J App Math, 1996, 56, 277-287.

RJ Wiltshire 1996 Perturbed Lie Symmetry and Systems of Non-linear Diffusion Equations. Journal of Nonlinear Mathematical Physics, 3, No 1/2, 130-138.

RJ Wiltshire and TJ Zastawniak 1996 Approximate Lie Symmetries for Diffusion Equations. Proc of the Sixth International Colloquium on Differential Equations. VSP International Publishers, Utrecht, The Netherlands. 351-358.

## Memberships

**Membership of External bodies:**

Member of Committee of Professors of Applied Mathematics in the UK

Fellow of the Institute of Physics

Member of the General Relativity and Gravitation Society

Member of the London Mathematical Society

Member of the National Conference of University Professors

Member of the British Soil Water Physics Group

## Research

**Main Research Interests:**

Integrable systems, symmetry methods

General theory of relativity, exact solutions, rotation

Partial differential equations

Non-linear mathematics with applications to the natural environment and biology

**Current Research Activity:**

Application and development of Lie, non-classical, Lie- Backlund and other symmetry methods to partial differential equations with environmental applications. There are collaborative links with the Departments of Mathematics, University of Cyprus and Departmento de matematica aplicada, Universidad Complutense de Madrid, Spain. Research students are also engaged in this work.

Exact solutions of Einstein’s equations with emphasis on solutions with shear. Also problems of rotation in particular solutions of Einstein’s equations embedded in Kerr empty space-time. These research developments follow a period of secondment in 2001 to the Department of Physics and Astronomy, University of Cardiff and also involve research student activity.

**If you are a journalist on deadline and you need to speak with** a member of university staff with particular expertise, please contact the Press Office.