Propagation of nonlinear acoustic fields in thermoviscous porous media

A family of generalized Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations, which is used in the study of the propagation of the sound beam and high-intensity focused ultrasound in a non-linear medium with dissipation and dispersion, is introduced. The new set of KZK equations, including the two-dimensional Zabolotskaya (K) used to describe the propagation of shear waves in nonlinear solids and the two-dimensional Zabolotskaya-Khokhlov (ZK) equations describing the propagation of weakly two-dimensional diffracting sound beams, are all reformulated in fractal dimensions based on the "product-like fractal geometry" approach. This approach has been introduced by Li and Ostoja-Starzewski in their analysis of nonlinear fractal dynamics in porous media. The set of nonlinear wave equations has been generalized by taking into account a nonlocal kernel due to its motivating implications in nonlinear acoustic wave theory. The solutions of particular algebraic equations in fractal dimensions have been obtained, and solitary wave solutions have been detected. Further details have been discussed accordingly.