Acknowledgments

I wish to thank Willy Hereman and Elizabeth Mansfield for discussions of computer techniques used when computing symmetries and Mark J. Ablowitz and Peter Clarkson for comments on the use of symmetries of differential equations. Thanks to James H. Curry for reading and commenting on numerous versions of this manuscript. Finally, I wish to thank the staff at Wolfram Research, especially Alexei Bocharov, for help with the intricacies of Mathematica.

Supported in part by the Department of Energy under grant DOE DE-FG03-94ER25194.