Tesis para optar al grado de Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas / Extreme waves generated in the ocean are of high importance because various maritime structures in the world, including ships, are confronted to this type of wave events, both in deep waters and in coastal areas. Some extreme waves correspond to wave phenomena generated in an atypical way in the ocean, also called monster waves, freak waves, rogue waves, extreme waves, solitons etc., since their generation differs from the common waves generated by wind. Assuming a slightly compressible ocean, the generation and analysis of acoustic-gravity waves (AGW or acoustic waves) in the ocean have been the subject of study for some time, because from them it is possible to obtain some information from the gravity wave, in this case a extreme wave that have generated them, and also to know other kind of phenomena induced by these AGW, as is the case of the bottom pressure. In the present work, a mathematical model has been developed which represents the generation and propagation of an extreme wave represented by a pressure change in the surface of the ocean considering compressible fluid, from which the generation and propagation of acoustic waves is induced. Since sound travels at a speed of 1500 m/s in the ocean, these waves arrive first at any observation point, allowing early detection of the extreme wave from the pressure in the oceanic bottom due to propagation of the acoustic wave. The theoretical development and two-dimensional numerical simulations are presented in the document. The implementation of this methodology and its results is relevant in the field of civil and maritime engineering in Chile since its high potential in coastal zones, due to the fact that for some years, the frequency of extreme wave events has been seen increased, and having an alternative detection system for extreme wave events can become a relevant factor in coastal management and natural disasters services. It is important to mention that this type of work has not been developed previously in Chile. / proyectos Centros de Excelencia Basal Conicyt PIA AFB 170001 CMM & UMI-CNRS 2807 y Fondecyt Regular 1171854