Engineering Science and Materials Commons^™

Solving Evolution Equations For Triad Interaction Of Shallow Water Waves, Qian Zhang

LSU Master's Theses

This study focuses on solving the evolution equations for triad interaction in shallow water waves. First, the evolution equations based on Boussinesq-type equations with Pad¨¦ approximant of the exact linear phase velocity using multi-scale perturbation analysis are derived. Next, methods of solving the complex equation directly, splitting the complex function into amplitude and phase functions, and splitting complex function into real and imaginary parts are implemented to solve the evolution equations. Then the fourth-order Runge-Kutta (RK4) numerical scheme is employed to solve the evolution equations, and corresponding numerical results of three wave interaction are presented demonstrating the sensitivity of the …