Application of Finite Element Method for Numerical Modeling of Solitary Waves by Peregrine Boussinesq Equations

From historical point of view, equations that have the capability of modeling the dispersion and nonlinearity characteristics of waves were first used by Peregrine in 1967 to analyze the experimental results of solitary waves. In year 1972, Peregrine, based on the equations that he had developed in year 1967, derived a new system of equations for modeling the waves in shallow waters. These equations later became the foundations for derivation of shallow water system of equations like that of Madsen-Sorensen in 1992. In the present article, an effort has been made to offer a suitable finite element method for numerical solution of Peregrine system of equations (1972) which would have the capability of solving other shallow water system of equations that would be derived based on the Peregrine system of equations.