The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy
| dc.creator | Ercolani, Nicholas M. | |
| dc.creator | Jin, Shan | |
| dc.creator | Levermore, C. David | |
| dc.creator | MacEvoy Jr, Warren D. | |
| dc.date | 2003-02-03 | |
| dc.date.accessioned | 2026-07-07T05:34:31Z | |
| dc.date.available | 2026-07-07T05:34:31Z | |
| dc.description | We present a numerical and theoretical study of the zero-dispersion limit of the focusing Zakharov-Shabat hierarchy, which includes NLS and mKdV flows as its second and third members. All the odd flows in the hierachy are shown to preserve real-valued data. We establish the zero-dispersion limit of all the nontrivial conserved densities and associated fluxes for these odd flows for a large class of real-valued initial data which includes all ``single hump'' initial data. In particular, it is done for the ``focusing'' mKdV flow. The method is based on the Lax-Levermore KdV strategy, but here it is carried out in the context of a nonselfadjoint spectral problem. We find that after an algebraic transformation the limiting dynamics of the mKdV equation is identical to that of the KdV equation. | |
| dc.identifier | https://arxiv.org/abs/nlin/0302003 | |
| dc.identifier | http://arxiv.org/abs/nlin/0302003 | |
| dc.identifier | IMRN 2003, no. 47, 2529-2564 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80396 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy | |
| dc.type | text |