@book{5ac48922ab024edeb435c75d9b3f036d,

title = "Prolongation structure of the Krichever-Novikov equation",

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.",

keywords = "MSC-37K30, MSC-35Q53, METIS-208635, MSC-37K10, EWI-3458, IR-65825",

author = "Sergei Igonine and Ruud Martini",

note = "Imported from MEMORANDA ",

year = "2002",

language = "Undefined",

isbn = "0169-2690",

series = "Memorandum Faculty Mathematical Sciences",

publisher = "Meetkundig en toegepast-algebraisch onderzoek",

number = "1638",

}