Simple and Solitary Waves in Materials

The following sections are included:

• Simple (Riemann) Waves

  • Simple waves in nonlinear acoustics

  • Simple waves in fluids

  • Simple waves in the general theory of waves

  • Simple waves in mechanics of electromagnetic continua

• Solitary Elastic Waves in Composite Materials

  • Simple solitary waves in materials

  • Chebyshev-Hermite functions

  • Whittaker functions

  • Mathieu functions

  • Interaction of simple waves. Self-generation

  • The solitary wave analysis

• New Hierarchy of Elastic Waves in Materials

  • Classical harmonic waves (periodic, nondispersive)

  • Classical arbitrary elastic waves (D'Alembert waves)

  • Classical harmonic elastic waves (periodic, dispersive)

  • Nonperiodic elastic solitary waves (with the phase velocity depending on the phase)

  • Simple elastic waves (with the phase velocity depending on the amplitude)