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Resonant Solutions of the Periodically Forced KdV Equation. Edition No. 1
- ID: 1899926
- August 2010
- 72 Pages
- VDM Publishing House
The periodically forced KdV equation can be used to model various physical wave phenomena. In the context of this research, the fKdV equation describes waves in a shallow tank of water. This work serves to extend previously published research from a basic case, to the general case, gaining an overall understanding of the matter. The publication consists of two primary parts. First, using boundary layer theory, and applying single scale perturbation, solutions are determined which take the functional form of either a squared hyperbolic secant, or a squared Jacobi-elliptic function, which then overlay a slow-varying wave. Second, the equation is numerically varied to yield a family of solutions which show the behaviour of the fKdV equation across resonant frequency. This research serves to better the understanding of the fKdV equation as it can be observed in a natural environment. It also gives rise to aspects worthy of further investigation.
has been an academician, an athlete, a linguist, and musician for most of his life. His mathematical interests began in highschool, and carried right on through university. Today he teaches calculus and linear algebra at Carleton University, while carrying on his research in quasi-linear partial differential equations.