Classification Of Self-Similar Solutions To A Generalized Burgers-Equation
Abbreviated Journal Title
J. Math. Anal. Appl.
Mathematics, Applied; Mathematics
A complete classification for the self-similar solutions to the generalized Burgers equation u(1)+u(beta)u(x)=t(N)u(xx) of the form u(t, n)=A(1)t(-(1-N)/2 beta)F(eta), where eta=A(2)xt(-(1+N)/2), A(2)=1/root 2A, and A(1)=(2A(2))(-1/beta) is obtained. The result gives an analytic justification to the result of Sachdev, Nair, and Tikekar  obtained through numerical and linear analysis. We also show the type of decay of the solutions at +/- infinity and the existence of periodic solutions if and only if N=-1 and beta=r/s where r and s are odd. (C) 1994 Academic Press, Inc.
Journal of Mathematical Analysis and Applications
"Classification Of Self-Similar Solutions To A Generalized Burgers-Equation" (1995). Faculty Bibliography 1990s. 1181.