On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach

Abstract

A manifestly $N=2$ supersymmetric coset formalism is introduced to describe integrable hierarchies. It is applied to analyze the super-NLS equation. It possesses an $N=2$ symmetry since it can be obtained from a manifest $N=2$ coset algebra construction. A remarkable result is here discussed: the existence of a Bäcklund transformation which connects the super-NLS equation to the equations belonging to the integrable hierarchy of one particular (the $a=4$) $N=2$ super-KdV equation. $N=2$ scalar Lax pair operators are introduced for both super-KdV and super-NLS.

10 pages, LaTex

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Cited by in corpus (26)

• Toward the construction of N=2 supersymmetric integrable hierarchies
• The Extended Supersymmetrization of the Multicomponent Kadomtsev--Petviashvilli Hierarchy
• N=4 super KdV hierarchy in N=4 and N=2 superspaces
• New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies
• Supersymmetric Drinfeld-Sokolov reduction
• New super KdV system with the N=4 SCA as the hamiltonian structure
• Manifestly Supersymmetric Lax Integrable Hierarchies
• N=4 Super NLS-mKdV Hierarchies
• N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
• The solution of the N=(0|2) superconformal f-Toda lattice
• Lax pairs for N=2,3 Supersymmetric KdV Equations and their Extensions
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• On Matrix KP and Super-KP Hierarchies in the Homogeneous Grading
• The N=2 supersymmetric Toda lattice and matrix models
• The Discrete Symmetry of the N=2 Supersymmetric Modified NLS Hierarchy
• A note on real forms of the complex N=4 supersymmetric Toda chain hierarchy in real N=2 and N=4 superspaces
• Extended N=2 supersymmetric matrix (1,s)-KdV hierarchies
• Dispersionless sTB
• Coset approach to the N=2 supersymmetric matrix GNLS hierarchies
• The Solution of the N=2 Supersymmetric f-Toda Chain with Fixed Ends
• Canonical gauge equivalences of the sAKNS and sTB hierarchies
• Integrable System Constructed out of Two Interacting Superconformal Fields
• A note on the third family of N=2 supersymmetric KdV hierarchies
• N=4 supersymmetric integrable systems
• Susy Hierarchies and Affine Algebras
• Hamiltonian structure and coset construction of the supersymmetric extensions of N=2 KdV hierarchy