Anomaly of linearization and auxiliary integrals
Boris Kruglikov
TL;DR
This paper explores the formal properties of the universal linearization operator, its relation to brackets of non-linear differential operators, and its application to auxiliary integrals in PDE compatibility reductions.
Contribution
It introduces new insights into the properties of the linearization operator and its role in the calculus of auxiliary integrals for PDEs.
Findings
Formal properties of the universal linearization operator clarified
Relation between linearization brackets and non-linear differential operators established
Application to auxiliary integrals in PDE compatibility reductions demonstrated
Abstract
In this note we discuss some formal properties of universal linearization operator, relate this to brackets of non-linear differential operators and discuss application to the calculus of auxiliary integrals, used in compatibility reductions of PDEs.
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