Integrable Systems Generated from Negative Order Hierarchy


Qiao Zhijun, The University of Texas-Rio Grande Valley


2017.08.09 09:30-11:00


Room 1202, Math Building


In this talk, I will track negative flows in the theory of integrable systems and solitons. Then we will show how to generate a negative order integrable hierarchy from the Lenard recursion operators, and then find the Lax pair for the entire hierarchy to guarantee the integrability. Interesting thing is that the peakon equation would be coming from the negative hierarchy. Amazing examples include the negative AKNS, negative KdV, CH, DP, cubic CH, inhomogeneous Burgers, and two-component short pulse equations etc. Particularly, real and complex short pulse equations can be derived from the negative AKNS.