Nonlinear Waves in Elastic Media
Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics.
Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws.
The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.
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On Plane Wave Problems in Elastic Media
Unsteady SelfSimilar Problems for Small Amplitude
TwoDimensional Steady Nonlinear Waves
anisotropy arbitrary asymptotics behavior boundary conditions Chapter characteristic velocities coefficients coincide components conservation laws considered const constant continuum mechanics coordinate system deformation depend determined eigenvalues eigenvector elastic media elastic potential energy equality evolutionary conditions evolutionary segments evolutionary shock expression extremum fast Riemann wave fast shock wave fast wave finite follows function incompressible media inequality initial point integral curve interaction intersection isotropic Jouget point linear longitudinal longitudinal wave magnetohydrodynamics matrix medium nonevolutionary obtained one-dimensional parameter plane plane-polarized polar quadrant quantity quasilongitudinal wave quasitransverse waves rectangle relations represented rotational discontinuity rotational waves satisfied second type Section self-similar problem shock adiabat shock velocity shown in Figure singular points slow shock wave slow waves small perturbations straight line strain tensor structure symmetrical tangent tensor transverse transverse waves ui-axis variables variations vector verse waves wave corresponding wave isotropy waves propagating