Backlund transformation for integrable hierarchies: example - mKdV hierarchy

30th International Colloquium on Group Theoretical Methods in Physics

Gomes, J.F.^1 ; Retore, A.L.^1 ; Spano, N.I.^1 ; Zimerman, A.H.^1

Instituto de Fisica Teorica IFT, Unesp Sao Paulo, Brazil^1

关键词: Algebraic structures;    Backlund transformations;    Gordon model;    Integrable hierarchy;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012039/pdf
DOI  :  10.1088/1742-6596/597/1/012039

来源: IOP

【 摘 要 】

In this note we present explicitly the construction of the mKdV hierarchy and show that it decomposes into positive and negative graded sub-hierarchies. We extend the construction of the Backlund transformation for the sinh-Gordon model to all other positive and negative odd graded equations of motion generated by the same affine algebraic structure. Some simple examples of solutions are explicitly verified to satisfy, in a universal manner, the Backlund transformations for the first few odd (positive and negative) sub-hierarchies.