Name
Abstract | ||
|---|---|---|
We consider infinite Fermi-Pasta-Ulam-type atomic chains with general convex potentials and study the existence of monotone fronts that are heteroclinic travelling waves connecting constant asymptotic states. Iooss showed that small amplitude fronts bifurcate from convex-concave turning points of the force. In this paper, we prove that fronts exist for any asymptotic states that satisfy certain constraints. For potentials whose derivative has exactly one turning point, these constraints mean precisely that the front corresponds to an energy conserving supersonic shock of the "p-system," which is the naive hyperbolic continuum limit of the chain. The proof is achieved via minimizing an action functional for the deviation from this discontinuous shock profile. We also discuss qualitative properties and the numerical computation of fronts. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/080743147 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
Fermi-Pasta-Ulam chain,heteroclinic travelling waves,conservative shocks | Mathematical optimization,Traveling wave,Heteroclinic cycle,Mathematical analysis,Continuum (design consultancy),Regular polygon,Supersonic speed,Amplitude,Classical mechanics,Monotone polygon,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
42 | 4 | 0036-1410 |
Citations | PageRank | References |
3 | 0.69 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Herrmann | 1 | 4 | 2.41 |
| Jens D. M. Rademacher | 2 | 16 | 5.06 |