Proposal report (MAT 530): the mathematical modelling of shallow water wave / Nik Nurfatinliyana Kamarudin, Nor Aniza Mohd Nasir and Nik Nur Izny Aqila Sapri

Waves are one of the most fundamental motions: waves on the water's surface and of earthquakes, waves along springs, light waves, radio waves, sound waves, waves of cloud, waves of crowds, brain waves, and so forth (Toda, 1989). Waves are recorded, and records are analyzed. In the case of sound waves and light waves, it is customary to analyze a wave as the sum of simple sinusoidal waves. This is the principal of linear superposition. However, when we observe water waves carefully, we can see that the linear superposition principle cannot be applied in general, except for very small amplitudes. The study of water waves of finite amplitude was one of the main topics.