Quantitative studies of nonlinear second sound in superfluidHe4

Experimental studies of the nonlinear evolution in time of planar second-sound pulses in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been carried out at temperatures 2 to 25 mK below ${\mathit{T}}_{\lambda }$. The pulse evolution in helium is compared to solutions of the Burgers equation, and corrections for the effect of the heater and bolometer substrates are made by numerical integration of the heat-diffusion equation with appropriate boundary conditions. Agreement between measured and calculated pulse shapes is found to be excellent. Fits to the data of the model are used to obtain the linear second-sound velocity. A new method for studying the critical behavior of second sound very close to ${\mathit{T}}_{\lambda }$, where nonlinear effects are always important, is suggested.