On the Kuznetsov equation and higher order nonlinear acoustics equations

Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation

“…Derivations of the Kuznetsov and HOAWE equations from fundamental principles can be found in Refs. [9][10][11]14]. We note that the linear wave equation neglects all nonlinear effects, the Kuznetsov equation represents nonlinear effects to the first power in , and the HOAWE includes both linear and quadratic terms in .…”

“…Consequently, it is valid for larger values of acoustic Mach number, and thus represents a more accurate model of acoustic wave propagation than Kuznetsov's equation. The equation as given by Söderholm [10,11] is as follows…”

“…More on this will be given later in this section, when we re-write this equation in a nondimensional form. A higher order acoustic wave equation (HOAWE) exists for gases [9][10][11]. This equation uses a more accurate equation of state, rather than the Taylor series expansion used in Kuznetsov's equation.…”

“…In our approach, we use a higher-order equation [9][10][11], which is valid up to higher acoustic Mach numbers than Kuznetsov's equation. Since the speed of the traveling wave depends on the acoustic Mach number, this high-order equation allows for a more accurate assessment of traveling wave velocities.…”

Nonlinear Wave Equation in Special Coordinates

“…In three-dimensional case, this is the nonlinear acoustic wave equation describing the waves in an isentropic gas flow for the non-dissipative case (see [2], [3], and [4]). …”