Abstract
In this paper, a super Wadati-Konno-Ichikawa (WKI) hierarchy associated with a 3×3 matrix spectral problem is derived with the help of the zero-curvature equation. We obtain the super bi-Hamiltonian structures by using of the super trace identity. Infinitely, many conserved laws of the super WKI equation are constructed by using spectral parameter expansions.
Highlights
The super extensions of the standard integrable systems in two-dimensional spacetime have been investigated for the recent several decades
We propose a super WKI hierarchy associated with a 3 × 3 matrix spectral problem, in which the first nontrivial member takes the following form: ut i64pffiffi−ffiffiffiuffiffiffiffiffiffiffi 1 + uv x
0, which is equivalent to the hierarchy of the super WKI equations
Summary
The super extensions of the standard integrable systems in two-dimensional spacetime have been investigated for the recent several decades. We propose a super WKI hierarchy associated with a 3 × 3 matrix spectral problem, in which the first nontrivial member takes the following form: ut. This spectral problem is an extension of the spectral problems associated with the WKI equation. We can refer to the two most recent results on the mixed method for the calculation of conservation laws studied in [29, 30]
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