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This is a Quantitative Study study.

October 8, 2025Open Access

Constraining all possible Korteweg–de Vries type hierarchies

Key Points

The study reveals constraints on integrable equations of the korteweg-de vries type, enhancing our understanding of symmetries.
Key findings indicate that generators of commuting subalgebras exhibit specific properties, contributing to the theory's infinite dimensional nature.
By exploring mutually commuting subalgebras, significant insights into the poisson bracket structure of conformal field theory are provided.
This research confirms the infinite dimensionality of recently identified commuting subalgebras, paving the way for future theoretical exploration.

Abstract

The Lie algebra of symmetries generated by the left-moving current j=∂−ϕ in the two-dimensional (2D) single scalar conformal field theory is infinite dimensional, exhibiting mutually commuting subalgebras. The infinite-dimensional mutually commuting subalgebras define integrable deformations of the 2D single scalar conformal field theory that preserve the Poisson bracket structure. We study these mutually commuting subalgebras, finding general properties that the generators of such a subalgebra must satisfy. Along the way, we derive constraints on integrable equations of the Korteweg–de Vries type. We also confirm that the recently found j=0,−1,−2 mutually commuting subalgebras are infinite dimensional.

Constraining all possible Korteweg–de Vries type hierarchies

Key Points

Abstract

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