ABSTRACT
In this chapter, the general expressions (solutions) for nonlinear long waves written in traveling waves will be presented. They are valid both for unbounded media and for finite resonators. These solutions are generalizations of d’Alembert’s solution for linear long waves. For finite resonators, traveling waves are expressed through own nonlinear functions of the resonators.
They can occur in a variety of elements of technology (structures) or can accompany a variety of natural phenomena. Therefore, it is not easy to even define what we mean by speaking about of extreme waves in so different circumstances. Generally speaking, this appearance can be associated with the degree of nonlinearity of the wave process under study. In a more practical sense, these waves can be determined by the degree to which their appearance is unexpected and by their extreme amplitude, which fundamentally distinguish these waves from linear waves.
As an example of such waves, we consider waves arising in various resonators. It is known that in a small neighborhood of resonant frequencies, there can be a very strong amplification of the excited wave. The waves themselves distort into unexpected, highly nonlinear forms.
