Journal
STUDIES IN APPLIED MATHEMATICS
Volume 131, Issue 1, Pages 72-103Publisher
WILEY
DOI: 10.1111/sapm.12007
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Funding
- NSF of China [11071157]
- RF of the DPHE of China [20113108110002]
- Shanghai Leading Academic Discipline Project [J50101]
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The usual Cauchy matrix approach starts from a known plain wave factor vector r and known dressed Cauchy matrix M. In this paper, we start from a determining matrix equation set with undetermined r and M. From the determining equation set we can build shift relations for some defined scalar functions and then derive lattice equations. The determining equation set admits more choices for r and M and in the paper we give explicit formulae for all possible r and M. As applications, we get more solutions than usual multisoliton solutions for many lattice equations including the lattice potential KdV equation, the lattice potential modified KdV equation, the lattice Schwarzian KdV equation, NQC equation, and some lattice equations in ABS list.
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