Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-11-26
Nonlinear Sciences
Exactly Solvable and Integrable Systems
27 pages, 6 figures
Scientific paper
We present a new representation of solutions of the Benjamin-Ono equation that are periodic in space and time. Up to an additive constant and a Galilean transformation, each of these solutions is a previously known, multi-periodic solution; however, the new representation unifies the subset of such solutions with a fixed spatial period and a continuously varying temporal period into a single network of smooth manifolds connected together by an infinite hierarchy of bifurcations. Our representation explicitly describes the evolution of the Fourier modes of the solution as well as the particle trajectories in a meromorphic representation of these solutions; therefore, we have also solved the problem of finding periodic solutions of the ordinary differential equation governing these particles, including a description of a bifurcation mechanism for adding or removing particles without destroying periodicity. We illustrate the types of bifurcation that occur with several examples, including degenerate bifurcations not predicted by linearization about traveling waves.
No associations
LandOfFree
An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An infinite branching hierarchy of time-periodic solutions of the Benjamin-Ono equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-273790