The mKdV and NLS hierarchies revisited
Jan-Cornelius Molnar, Yannick Widmer
TL;DR
This paper demonstrates how the entire mKdV hierarchy can be derived as restrictions of the NLS hierarchy using normal form theory, revealing a deep connection between these integrable systems.
Contribution
It provides a novel framework linking the mKdV and NLS hierarchies through restrictions, enhancing understanding of their structural relationship.
Findings
mKdV hierarchy expressed as restrictions of NLS hierarchy
Normal form theory used to prove the connection
Deepens understanding of integrable systems' structure
Abstract
The purpose of this paper is to express the entire hierarchy of mKdV vector fields as restrictions of vector fields in the NLS hierarchy. The result is proved using the normal form theory of the two equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Numerical methods for differential equations