Unimodular matrix on shallow water wave theory. Unimodularity through matrix method
The matrix method used in many studies of wave theory, for easy calculations, is described and used in the shallow water
breaking theory. We deal with shallow water wave breaking and the method of unimodular matrix. Introducing a class of nonlinear
water waves, the solution in the stratification regions using matrix method through unimodularity is given.
In this paper we present the stratification approximated by n-layers. Our method firstly involves a 2x2 matrix. Taking the production
of n 2x2 matrices we choose the layers with linear variation. The main part of our work covers the fact that energy conservation law is
satisfied. For this the unimodularity of the matrices is used. The models are tested against experiments concerning periodic wave
transformation. The density and the speed of waves vary exponentially with depth. We conclude with experiments and some important
conclusions.
breaking theory. We deal with shallow water wave breaking and the method of unimodular matrix. Introducing a class of nonlinear
water waves, the solution in the stratification regions using matrix method through unimodularity is given.
In this paper we present the stratification approximated by n-layers. Our method firstly involves a 2x2 matrix. Taking the production
of n 2x2 matrices we choose the layers with linear variation. The main part of our work covers the fact that energy conservation law is
satisfied. For this the unimodularity of the matrices is used. The models are tested against experiments concerning periodic wave
transformation. The density and the speed of waves vary exponentially with depth. We conclude with experiments and some important
conclusions.