Physical Sciences and Mathematics Commons^™

Analysis Of Nonlinear Dispersive Model Equations, Jacob Grey

LSU Doctoral Dissertations

In this work we begin with a brief survey of the classical fluid dynamics problem of water waves, and then proceed to derive well known evolution equations via a Hamiltonian Variational approach. This method was first introduced in the seminal work of Walter Craig, et al. \cite{CG}. The distinguishing feature of this scheme is that the Dirichlet-Neumann operator of the fluid domain appears explicitly in the Hamiltonian. In the second and third chapters, we utilize the Hamiltonian perturbation theory introduced in \cite{CG} to derive the Benjamin-Bona-Mahony (BBM) and Benjamin-Bona-Mahony-Kadomtsev-Petviashvili (BBM-KP)equations. Finally, we briefly review the existence theory for their corresponding …

On Nonlinear Generalizations Of The Kdv And Bbm Equations From Long Range Water Wave Theory, Timothy A. Smith

Publications

A generalization of the famous KdV and BBM equation are considered with a new nonlinear term. Sufficient conditions of solvability, existence and uniqueness are established.

On Existence And Uniqueness Results For The Bbm Equation With Arbitrary Forcing Terms, Timothy A. Smith

Publications

The problem of classical solutions for the regularized long-wave equation is considered where various additional forcing terms are introduced which are often required for physical modifications in the wave theory. Sufficient conditions of solvability and existence are established and then these conditions are related to the structure of the forcing terms under consideration.

On Existence And Uniqueness Results For The Bbm Equation With Arbitrary Forcing Terms, Timothy A. Smith

Timothy Smith