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Comments on the Negative grade KdV Hierarchy

by Y. F. Adans, J.F. Gomes, G.V. Lobo and A.H. Zimerman

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Submission summary

Authors (as registered SciPost users): Jose Gomes
Submission information
Preprint Link: scipost_202212_00040v2  (pdf)
Date accepted: 2023-08-11
Date submitted: 2023-02-15 14:16
Submitted by: Gomes, Jose
Submitted to: SciPost Physics Proceedings
Proceedings issue: 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022)
Ontological classification
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representation and maps the Lax operator of the mKdV into its couterpart within the KdV setting. Each odd negative KdV flow is obtained from an odd and its subsequent even negative mKdV flows. The negative KdV flows are shown to inherit the two different vacua structure that characterizes the associated mKdV flows.

List of changes

We have made all requested changes regarding grammar errors, typos, punctuation, etc

We have rewritten text between eqns. (17) and (22) in order to clarify the the different vacuum structures employed in the paper.

Published as SciPost Phys. Proc. 14, 014 (2023)

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