Fundamental models in nonlinear acoustics part I. Analytical comparison

This work is concerned with the study of fundamental models from nonlinear acoustics. In Part I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In particular, a rigorous justification of two classical models, the Kuznetsov and Westervelt equations, retained as limiting systems for vanishing thermal conductivity and consistent initial data, is given. Numerical comparisons that confirm and complement the theoretical results are provided in Part II.

On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations

We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equationutt+fuut=div(gugrad u)with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases.