Name
Abstract | ||
|---|---|---|
A symmetry of a differential equation is a transformation which leaves invariant its family of solutions. As the functional form of a member of a class of differential equations changes, its symmetry group can also change.We give an algorithm for determining the structure and dimension of the symmetry group(s) of maximal dimension for classes of partial differential equations. It is based on the application of differential elimination algorithms to the linearized equations for the unknown symmetries. Existence and Uniqueness theorems are applied to the output of these algorithms to give the dimension of the maximal symmetry group.Classes of differential equations considered include ODE of form uxx = ƒ(x, u, ux), Reaction-Diffusion Systems of form ut - uxx = ƒ(u, v), vt - vxx = g(u, v), and Nonlinear Telegraph Systems of form vt = ux, vx = C(u, x)ux + B(u, x). |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1145/345542.345651 | ISSAC |
Keywords | Field | DocType |
maximal symmetry group,form ut,functional form,differential elimination algorithm,differential equation,form uxx,partial differential equation,form vt,differential equations change,symmetry group,tensor notation,linear equations,notation,bra ket notation | Discrete mathematics,Differential equation,Symmetry group,Nonlinear system,Separable partial differential equation,First-order partial differential equation,Differential algebraic equation,Partial differential equation,Homogeneous space,Mathematics | Conference |
ISBN | Citations | PageRank |
1-58113-218-2 | 1 | 0.58 |
References | Authors | |
8 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gregory J. Reid | 1 | 6 | 2.92 |
| Allan D. Wittkopf | 2 | 22 | 2.87 |