Exact N-wave solutions of generalized Burgers equations

Exact N-wave solutions for the generalized Burgers equation u(t) + u(n)u(x) + (j/2t + alpha) u + (beta + gamma/x) u(n+1) = delta/2u(xx), where j, alpha, beta, and gamma are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.