Harmonic Wave Systems is the first
textbook about the computational method of Decomposition in Invariant
Structures (DIS) that generalizes the analytical methods of separation of
variables, undetermined coefficients, asymptotic expansions, and series
expansions. In recent years, there has been a boom in publications on
propagation of nonlinear waves described by a fascinating list of partial
differential equations (PDEs). The vast majority of wave problems are reducible
to one-dimensional ones in propagation variables. However, a list of
publications with two- and three-dimensional applications of the DIS method is
brief.
The book
offers a comprehensive and rigorous treatment of the DIS method in two and
three dimensions using the PDE approach to the Helmholtz decomposition that
provides the most general background for mathematical modelling of harmonic
waves in fluid dynamics, electrodynamics, heat transfer, and other numerous
areas of science and engineering, which are dealing with propagation and
interaction of N internal
waves.