Name
Abstract | ||
|---|---|---|
A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg - Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equation's symmetry group. With the method used, relative periodic solutions are represented by a space-time Fourier series modified to include the symmetry group element and are sought as solutions to a system of nonlinear algebraic equations for the Fourier coefficients, group element, and time period. The 77 relative periodic solutions found for the CGLE exhibit a wide variety of temporal dynamics, with the sum of their positive Lyapunov exponents varying from 5.19 to 60.35 and their unstable dimensions from 3 to 8. Preliminary work indicates that weighted averages over the collection of relative periodic solutions accurately approximate the value of several functionals on typical trajectories. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/040618977 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | Field | DocType |
relative periodic solutions,Ginzburg-Landau equation,spectral-Galerkin method,chaotic pattern dynamics | Differential equation,Nonlinear system,Symmetry group,Mathematical analysis,Periodic boundary conditions,Algebraic equation,Fourier series,Periodic graph (geometry),Periodic sequence,Mathematics | Journal |
Volume | Issue | ISSN |
4 | 4 | 1536-0040 |
Citations | PageRank | References |
2 | 0.66 | 4 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vanessa Lopez | 1 | 2 | 0.99 |
| Philip Boyland | 2 | 2 | 0.66 |
| Michael T. Heath | 3 | 366 | 73.58 |
| Robert D. Moser | 4 | 57 | 8.55 |