Propagation of nonlinear acoustic waves in bimodular media with linear dissipation

A new equation and exact solutions describing focal fields in media with modular nonlinearity

“…Note that the analytical smoothing described above is consistent with the results of numerical modeling performed by Nazarov and co-workers for other equations with modular nonlinearity [17,21]. The construction of smoothed solutions can be done using the standard method of matched asymptotic expansions.…”

“…Studies of plane waves in media with modular nonlinearity described by modified Burgers-type equations started recently [17]. These media have different elastic constants for the tensile and compressional deformations.…”

“…The physical meaning of (18) is the conservation of linear momentum of a volume of the medium in which the wave propagates [4]. These additional conditions make it possible to calculate the constant D in formula (17), as well as the connection between parameters γ and β. The final form of this solution is: The solution (19) for one period of wave is shown in Fig.…”

Equation admitting linearization and describing waves in dissipative media with modular, quadratic, and quadratically cubic nonlinearities

“…As and grow, smoothing is enhanced (see the curves for and 0.2). Note that the described smoothing of singularities agrees with the numerical results obtained by Nazarov's research team [10][11][12]. Smoothed solutions can also be constructed by applying the standard method of matched asymptotic expansions (see, e.g., [14]).…”

“…Recently, studies were initiated of waves in media with a modular nonlinearity ( , ) [10][11][12], which exhibit different elasticity properties under tensile and compressive strains. Examples of such materials are reinforced polymers and concretes (see [13,Chapter 1,Section 10]).…”