A generalization of the Lax equation
โ Scribed by Maria Przybylska
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 215 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0393-0440
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โฆ Synopsis
We propose a generalization of the standard Lax equation defined by means of an arbitrary action of a Lie algebra on a matrix differential manifold. We analyze properties of obtained equation and show examples with physical applications. In particular, certain constructions of Hamiltonian subclasses of this generalized Lax equation are described.
๐ SIMILAR VOLUMES
A new production form for a hierarcltJ. of nonlinear evolutiorz equations (NLEEs) is given in this paper. The ,form corttairrs productions of isospectral and mm-isospectral hierarchy. 'Under this .fornt a .generaked structure of Las represerztlhms for the hierarchy of NLEEs is this presellted. As a
It is proved that the function deรฟned by the inรฟmum-based Lax formula (for viscosity solutions) provides a solution almost everywhere in x for each รฟxed t ยฟ 0 to the Hamilton-Jacobi, Cauchy problem ut + 1 2 โu 2 = 0; u(x; 0 + ) = v(x); where the Cauchy data function v is lower semicontinuous on rea