Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law

Abstract

A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scala 1D equation $u_t+[f(u){]}_x=0$, for any flux $f(u)$ and initial condition $u_0(x)$ that are analytic. This formula is valid at least as long as $u$ remains analytic.