From the solution of the Tsarev system to the solution of the Whitham equations
| dc.creator | Grava, T. | |
| dc.date | 2000-07-12 | |
| dc.date.accessioned | 2026-07-07T05:32:57Z | |
| dc.date.available | 2026-07-07T05:32:57Z | |
| dc.description | We study the Cauchy problem for the Whitham modulation equations for monotone increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2,... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so called hodograph transform introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each $g>0$, we construct the unique solution of the Tsarev system, which matches the genus $g+1$ and $g-1$ solutions on the transition boundaries. Next we characterize initial data such that the solution of the Whitham equations has genus $g\leq N$, $N>0$, for all real $t\geq 0$ and $x$. | |
| dc.description | Latex2e 41 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0007016 | |
| dc.identifier | http://arxiv.org/abs/nlin/0007016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79839 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | From the solution of the Tsarev system to the solution of the Whitham equations | |
| dc.type | text |