WAVE PROPAGATION IN A NON-LOCAL MEDIUM WITH NON-LINEAR ENERGY SOURCES

The dynamics of waves in the “medium – energy source” system are considered. The volumetric energy source is a nonlinear function of temperature. An example of a nonclassical material is a medium with weak spatial nonlocality. The mathematical model of such processes is a wave equation containing an additional term with a fourth-order spatial derivative. Two types of nonlinear sources are discussed: trigonometric nonlinearity (“double sine-Gordon”, “sine-Gordon”) and polynomial (fifth-degree) nonlinearity. Exact analytical solutions are constructed, representing a kink (wave overturn) and a solitary wave (either a trough or an elevation). A distinctive feature of the constructed kink wave is that the argument of the arctangent is a fractional-rational function of the exponential wave coordinate. The solitary wave is a fractional-rational function of the wave coordinate. The regularities of the influence of the medium's nonlocality parameter on the subsonic and supersonic wave propagation speeds are determined. The correlation between the “analytical structure of the source function – wave profile” is studied. A detailed illustration of subsonic and supersonic wave propagation regimes is provided, depending on the non-monotonic and sign-changing properties of the source function