We study the Cauchy problem for the Whitham modulation equations for 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 transformation 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.

From the solution of the Tsarev system to the solution of the Whitham equations / Grava, Tamara. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - 4:1(2001), pp. 65-96. [10.1023/A:1011892100149]

From the solution of the Tsarev system to the solution of the Whitham equations

Grava, Tamara
2001-01-01

Abstract

We study the Cauchy problem for the Whitham modulation equations for 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 transformation 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.
2001
4
1
65
96
Grava, Tamara
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13318
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