Similarity Solutions of Nonlinear Partial Differential Equations

The method of similarity solutions for solving nonlinear partial differential equations has produced a plentiful harvest of results since Birkhoff called attention to it in 1950. The general references in the bibliography at the end of this book cite hundreds of successful individual works. In spite of this success, the method is still not as widely known as equally fruitful methods for solving linear partial differential equations, e.g., separation of variables or Laplace transforms. To popularize the method of similarity solutions, to teach it as a practical technique, to make it a part of the daily armament of the technologist, is the goal of this book.
In harmony with this goal, I have kept the book short and refrained from any great mathematical rigor. To keep the pace swift, I have avoided making an exhaustive survey of the literature. The illustrative examples are drawn mainly from my own work. For most partial differential equations, I have sketched as briefly as possible the physical background. I have not dwelt on it overmuch because our concern here is with the mathematics, but I have not omitted it either because I believe that knowing the physical background helps make clear why we proceed as we do.