Modal analysis of long wave equations

This work studies the use of modal expansion approximations of solutions of model long wave equations. Such model equations are of interest to oceanographers and engineers because they describe the propagation of surface water waves, used in near-shore models of sandbar formation. General theoretical results are derived for standard long wave models in the form of dispersive, nonlinear partial differential equations. Particular numerical results are computed for such model equations, including the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the Benjamin-Ono equation, among others.