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Abstract We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of $L^2$ bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but also under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.
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This content will become publicly available on February 28, 2026
Geometry of Integrable Linkages
In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic “no-slip” conditions. Using constructs from sub-Riemannian geometry, we look for geodesics corresponding to linkage motion with these constraints (“tricycle kinematics”). The paths of the three vertices turn out to be critical points for functionals which appear in the hierarchy of conserved quantities for the planar filament equation, a well known completely integrable evolution equation for planar curves. We show that the geodesic equations are completely integrable, and present a second connection to the planar filament equation.
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- Award ID(s):
- 2005444
- PAR ID:
- 10588151
- Publisher / Repository:
- AMR
- Date Published:
- Journal Name:
- Journal of Experimental Mathematics
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2998-4114
- Page Range / eLocation ID:
- 94 to 123
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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