Generalized nonisospectral super integrable hierarchies. (14th April 2019)

• Record Type: Journal Article
• Authors: Yu, Jing; Zhou, Shouhang; Han, Jingwei; He, Jingsong
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 12(2019)
• Page Start: 4213
• Page End: 4224
• Publication Date: 2019-04-14
• Subjects: generalized nonisospectral super AKNS hierarchy -- generalized nonisospectral super Dirac hierarchy -- Lie superalgebra; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5640
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : For the Lie superalgebra B (0, 1), we choose a set of basis matrices. Then we consider a linear combination of the basis matrices, which is exactly the spectral matrix of the spatial part for the super Ablowitz‐Kaup‐Newell‐Segur (AKNS) hierarchy. The compatible condition of the spatial and temporal spectral problems leads to the well‐known zero curvature equation. Here, when the spectral parameter is independent (dependent) of temporal parameter, we obtain isospectral (nonisospectral) super AKNS hierarchy. Furthermore, we derive the generalized nonisospectral super AKNS hierarchy (GNI‐SAKNS). As another example, similar method is successfully applied to the super Dirac hierarchy, and we obtain the generalized nonisospectral super Dirac hierarchy (GNI‐SD).