Potential symmetries of inhomogeneous nonlinear diffusion equations
2000 ◽
Vol 61
(3)
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pp. 507-521
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Keyword(s):
In this paper potential symmetries are sought of the inhomogeneous nonlinear diffusion equations ut = x1−M[xN−1f (u) ux]x. The functional forms of f (u) that admit such symmetries are completely classified. A complete list is presented of the symmetries, which depend on the values of the parameters M and N. We give examples of similarity solutions using potential symmetries. In some cases, the potential symmetries enable us to convert non–invertible mappings of nonlinear partial differential equations to linear ones.
1988 ◽
Vol 11
◽
pp. 531-534
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2009 ◽
Vol 50
(1)
◽
pp. 013502
◽