直接法的推广与广义Burgers方程的条件对称约化

A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.     

Letters to the Editor

Nonperiodic functions can sometimes be changed into periodic ones by appropriately restricting the original domain of definition of the function. This important aspect in the teaching of periodicity is explicated through the problem of finding all n for which cos n2 = 2cos n sin4n.

     

Letters to the editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chief, Chandler Davis.     

Reply to the discussion

Alan Lee adds to the topic and work of the paper by providing highly insightful discussion and new results. I thank him.