Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

Journal Article · Sun May 01 04:00:00 EDT 1994 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.530543· OSTI ID:5019502

Grant, A K; Rosner, J L ^[1]

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1. Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States)

The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.

• DOE Contract Number: FG02-90ER40560
• OSTI ID: 5019502
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 35:5; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120* -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVERSE SCATTERING PROBLEM
KORTEWEG-DE VRIES EQUATION
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
QUANTUM MECHANICS
QUASI PARTICLES
SOLITONS
SUPERSYMMETRY
SYMMETRY
TRANSFORMATIONS