Mathematics, Syiah Kuala University
This paper aims to describe a deterministic generation of extreme waves in a typical towing tank. Such a generation involves an input signal to be provided at the wave maker in such a way that at a certain position in the wave tank, say at a position of a tested object, a large amplitude wave emerges. For the purpose, we consider a model called a spatial-NLS describing the spatial propagation of a slowly varying envelope of a signal. Such model has an exact solution known as (spatial) Soliton on Finite Background (SFB) that is a non-linear extension of Benjamin-Feir instability. This spatial-SFB is characterized by wave focusing leading to almost time periodic extremes that appear between phase singularities. Although phase singularities and wave focusing has been the subject of number of studies, this spatial-SFB written in the field variables has many interesting properties among which are the existence of many critical values related to the modulation length of the monochromatic signal in the far fields. These properties will be used to in choosing parameters for a deterministic generation of extreme waves. Some example of such a generation in realistic variables will be displayed.