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Similarity analysis of differential equations by Lie group
Na, Tsung-Yen; Hansen, Arthur G.
Na, Tsung-Yen; Hansen, Arthur G.
1971-12
Citation:Na, Tsung Y., Hansen, Arthur G. (1971/12)."Similarity analysis of differential equations by Lie group." Journal of the Franklin Institute 292(6): 471-489. <http://hdl.handle.net/2027.42/33514>
Abstract: Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analyses in a broader sense--namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations--is given with new and very general methods evolved for deriving the possible groups of transformations.