Yurchuk V. Theory of solitary waves in nonlinearly elastic materials

In this thesis, some fragment of the theory of solitary waves in the deforming elastically nonlinearly materials is studied. The main attention is drawn to evolution of the initial profile of solitary waves. A nonlinearity is based on introduction of the Murnaghan potential and subsequent allowance for the quadratic and cubic nonlinearities in the obtained wave equations. The plane longitudinal and transverse and cylindrical radial waves are studied.The types of initial profile of solitary wave are considered that are close to the wave profiles in materials observed in experiments and are described analytically by the known from the mathematical physics functions. An approximate approach to solving the nonlinear wave equations is applied and developed what allowed to analyze numerically the stated problems on propagation of waves.