Symmetries and conservation laws of the generalized Krichever-Novikov equation

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A computational classification of contact symmetries and higher-order local symmetries that do not commute with t, x, as well as local conserved densities that are not invariant under t, x is carried out for a generalized version of the Krichever-Novikov (KN) equation. Several new results are obtained. First, the KN equation is explicitly shown to have a local conserved density that contains t, x. Second, apart from the dilational point symmetries known for special cases of the KN equation and its generalized version, no other local symmetries with low differential order are found to contain t, x. Third, the basic Hamiltonian structure of the KN equation is used to map the local conserved density containing t, x into a nonlocal symmetry that contains t, x. Fourth, a recursion operator is applied to this nonlocal symmetry to produce a hierarchy of nonlocal symmetries that have explicit dependence on t, x. When the inverse of the Hamiltonian map is applied to this hierarchy, only trivial conserved densities are obtained.

Avdonina, E. D.Ufa State Aviat Tech Univ, Russia. (author)
Gainetdinova, A.Ufa State Aviat Tech Univ, Russia. (author)
Galiakberova, L. R.Ufa State Aviat Tech Univ, Russia. (author)
Ibragimov, NailBlekinge Tekniska Högskola,Institutionen för matematik och naturvetenskap(Swepub:bth)nib (author)
Wolf, T.Brock University, Canada. (author)
Brock University, Canada.Ufa State Aviat Tech Univ, Russia. (creator_code:org_t)

In:Journal of Physics A: Institute of Physics Publishing (IOPP)49:101751-81131751-8121

By the author/editor: Anco, S.; Avdonina, E. D.; Gainetdinova, A.; Galiakberova, L. ...; Ibragimov, Nail; Wolf, T.

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