Classification of Self Similar Solutions to a Generalized Burgers Equation

A complete classification for the self-similar solutions to the generalized Burgers equation ut+uβux=tNuxx of the form u(t, η)=A1t−(1−N)/2βF(η), where η=A2xt−(1+N)/2, [formula], and A1=(2A2)−1/β is obtained. The result gives an analytic justification to the result of Sachdev, Nair, and Tikekar [3] obtained through numerical and linear analysis. We also show the type of decay of the solutions at ±∞ and the existence of periodic solutions if and only if N=−1 and β=r/s where r and s are odd.