Painleve Analysis And Special Solutions For A Class Of Cahn-Hilliard Equations
Abbreviated Journal Title
Can. J. Phys.
PARTIAL-DIFFERENTIAL EQUATIONS; LINEAR EVOLUTION-EQUATIONS; BACKLUND; TRANSFORMATION; P-TYPE; PROPERTY; CONNECTION; INVARIANT; Physics, Multidisciplinary
A Painleve analysis of a family of Cahn-Hilliard equations (with diffusion coefficients of the form D(U) = SIGMA-m(i=0) (D(i)U(i)) is performed. For m = 2, the equation fails the Painleve test. Of the other cases of physical interest, the case m = 1 has only the conditional Painleve property; while the cases m = 3, 4 are weak Painleve, suggesting that the equation is partially integrable for these cases. For the cases m = 1 and m = 2, an auto-Backlund transformation between two solutions is constructed, leading to classes of analytical solutions of the equations. Special analytical solutions for all m greater-than-or-equal-to 3 are also constructed.
Canadian Journal of Physics
"Painleve Analysis And Special Solutions For A Class Of Cahn-Hilliard Equations" (1992). Faculty Bibliography 1990s. 417.