The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the surface wave solutions. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the frequency equation of Rayleigh wave. The numerical values of the non-dimensional speed of Rayleigh wave speed are computed for different values of frequency...

A new formalism of spectral filtering for the description of the modulation processes is proposed. The method allows one to study the classical problem of multi-phase modulations in dispersive systems. In the present paper, deepwater waves are considered. Spectral filtering results in a system of coupled equations that describe the modulations of the carrier wave and its harmonics. The formalis...

Conventional definitions of velocities associated with the propagation of modulated waves cannot clearly describe the behavior of the wave packet in a multidimensional dispersive medium. The conventional definition of the phase velocity, which is perpendicular to the wave front, is a special case of the generalized phase velocity defined in this work, since there exist an infinite number of sol...

We show that diffraction stack migration can be used to estimate the distribution of near-surface faults. The assumption is that near-surface faults generate detectable back-scattered surface waves from impinging surface waves. The processing steps are to isolate the back-scattered surface waves, and then migrate them by diffraction migration using the surface wave velocity as the migration vel...

It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive water wave system, and auto-Bäcklund transformations for coupled three-component KdVtype ...

A model for the formation and evolution of longshore sand ridges in waters deeper than the shoaling region suggests that a possible but by no means exclusive agent for the formation of these bars are weakly nonlinear dispersive long waves. The model describes how these water waves, which are represented by wave packets, and a sandy bottom topography, conspire to produce sand ridges. This study ...

In the previous three chapters, we built up the foundation for our study of waves. In the remainder of this book, we’ll investigate various types of waves, such as waves on a string, sound waves, electromagnetic waves, water waves, quantum mechanical waves, and so on. In Chapters 4 through 6, we’ll discuss the properties of the two basic categories of waves, namely dispersive waves, and non-dis...