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 scalar 1D equation $u_t+{\left[f\left(u\right)\right]}_x=0$, for any flux $f\left(u\right)$ and initial condition $u_0\left(x\right)$ that are analytic. This formula is valid for some times $t>0$, $u$ remaining analytic.