Nonlinear second sound in solids

We study the nonlinear propagation of thermal waves in rigid heat conductors using a model introduced by Ruggeri et al. We derive the lowest-order nonlinear corrections to the wave speed and show that the quadratic nonlinearity can be small for NaF and Bi. The smallness of the nonlinear steepening parameter complicates the wave dynamics, allowing for both forward and backward steepening waves within the same pulse. We show that this mixed condition places limits on the size of admissible discontinuities; we then argue that this limit on the size of shock waves limits the arrival times of thermal signals. Using this, we propose an experiment to measure arrival times to look for this limiting behavior.