Abstract
The concept of homology (SIAM J. Appl. Math., 40 (1981), pp. 191–207) is generalized to an arbitrary nonlinear diffusion equation. A large class of self-homologous diffusion coefficients is introduced and used to examine possible changes in initial and boundary conditions through homologous transformations. Generalized homology is shown to be identical to Bäcklund transformations.
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