Home About Upload Latest Additions Statistics Contact
UT Proceedings
UT Student Theses
Dutch Academic Output Dutch Dissertations EU Publications (OpenAIRE)
Printversion
Advanced search

Prolongation structure of the Krichever-Novikov equation

Share/Save/Bookmark

Igonin, S. and Martini, R. (2002) Prolongation structure of the Krichever-Novikov equation. [Report]

[img]
Preview
PDF
193Kb
Abstract:
We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on $u,\,u_x,\,u_{xx},\,u_{xxx}$ for the Krichever-Novikov equation $u_t=u_{xxx}-3u_{xx}^2/(2u_{x})+p(u)/u_{x}+au_{x}$ in the case when the polynomial $p(u)=4u^3-g_2u-g_3$ has distinct roots. We prove that there is a universal prolongation algebra isomorphic to the direct sum of a commutative $2$-dimensional algebra and a certain subalgebra of the tensor product of $\mathfrak{sl}_2(\mathbb{C})$ with the algebra of regular functions on an affine elliptic curve. This is achieved by identifying this prolongation algebra with the one for the anisotropic Landau-Lifshitz equation. Using these results, we find for the Krichever-Novikov equation a new zero-curvature representation, which is polynomial in the spectral parameter in contrast to the known elliptic ones.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:http://purl.utwente.nl/publications/65825
Export this item as:BibTeX
EndNote
HTML Citation
Reference Manager

 

Repository Staff Only: item control page