Symmetry analysis and hidden variational structure of Westervelt’s equation in nonlinear acoustics

Westervelt's equation is a nonlinear wave that widely used to model the propagation of sound waves in compressible medium, with one important application being ultra-sound human tissue. Two fundamental aspects this -- symmetries and conservation laws are studied present work by modern methods. Numerous results obtained: new conserved integrals; potential systems yielding hidden nonlocal laws; mapping undamped case into linear equation; exact solutions arising from mapping; variational structures, including Lagrangian Hamiltonian; recursion operator Noether operator; contact symmetries; higher-order laws.