Rational Solutions to the ABS List: Transformation Approach

@article{Zhang2017RationalST,
  title={Rational Solutions to the ABS List: Transformation Approach},
  author={Dan-da Zhang and Da-jun Zhang},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2017},
  volume={13},
  pages={078}
}
  • Dan-da Zhang, Da-jun Zhang
  • Published 2017
  • Physics, Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1($\delta$), H3($\delta$), H2 and H1 in the Adler-Bobenko-Suris list. B\"acklund transformations between these lattice equations are used. All these rational solutions are related to a unified $\tau$ function in Casoratian form which obeys a bilinear superposition formula. 
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