A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms

Symmetry Integrability and Geometry-Methods and Applications

article

Mike C. Hay¹ 

[1] Institute of Mathematics for Industry, Kyushu University, Ito Campus

关键词: discrete integrable systems;    Lax pairs;   

DOI  :  10.3842/SIGMA.2011.089

来源: National Academy of Science of Ukraine

【 摘 要 】

We expand the completeness study instigated in [ J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms within the Lax matrices to be zero. We cover all possible Lax pairs of this type and find a new third order equation that can be reduced to special cases of the non-autonomous lattice KdV and lattice modified KdV equations among others.

【 授权许可】

Unknown