126 citations · 181 across the 14 of their papers we have counts for
6 papers · 1 filter
Symmetries of a class of Nonlinear Third Order Partial Differential Equations
P. A. Clarkson, E. L. Mansfield, T. J. Priestley
In this paper we study symmetry reductions of a class of nonlinear third order partial differential equations where , ,…
Symmetries and Exact Solutions of a 2+1-dimensional Sine-Gordon System
P. A. Clarkson, E. L. Mansfield, A. E. Milne
We investigate the classical and nonclassical reductions of the -dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalisation of the sine-Gordo…
Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations
Peter A. Clarkson, Elizabeth L. Mansfield
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation $$u_{xxxt} + αu_x u_{xt} + βu_t u_{xx} - u_{xt} - u_{xx} = 0,\eqno(1)$$ wher…
On a Shallow Water Wave Equation
Peter A. Clarkson, Elizabeth L. Mansfield
In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud.…
Algorithms for the Nonclassical Method of Symmetry Reductions
Peter A. Clarkson, Elizabeth L. Mansfield
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Co…
Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat Equations
Peter A. Clarkson, Elizabeth L. Mansfield
Classical and nonclassical symmetries of the nonlinear heat equation $$u_t=u_{xx}+f(u),\eqno(1)$$ are considered. The method of differential Gröbner bases is used both to find the…