Supersymmetric quantum mechanics and the Korteweg-de Vries hierarchy

Abstract

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.

16 pages, latex, EFI 93/20

Cited by in corpus (14)

• Chiral fermions, orbifolds, scalars and fat branes
• Invisibility in non-Hermitian tight-binding lattices
• All about the Static Fermion Bags in the Gross-Neveu Model
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• Invisible defects in complex crystals
• Conditional symmetry and spectrum of the one-dimensional Schrödinger equation
• Position-dependent mass models and their nonlinear characterization
• Absence of Floquet scattering in oscillating non-Hermitian potential wells
• Non-Hermitian invisibility in tight-binding lattices
• Hierarchy of QM SUSYs on a Bounded Domain
• Hidden symmetries for transparent de Sitter space
• Free Particle to Complex KdV breathers through Isospectral Deformation