Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 473, Issue 2203, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2017.0233
Keywords
trigonal curve; Baker-Akhiezer function; algebro-geometric solution
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Funding
- National Natural Science Foundation of China [11371326, 11371086, 11301331]
- NSF [DMS-1664561]
- Shanghai University of Electric Power
- Shanghai Second Polytechnic University
- National Natural Science Foundation of China [11371326, 11371086, 11301331]
- NSF [DMS-1664561]
- Shanghai University of Electric Power
- Shanghai Second Polytechnic University
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This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi coordinates associated with Lax pairs, upon determining the Riemann theta function representations of the Baker-Akhiezer functions, and generate algebro-geometric solutions to soliton hierarchies in terms of the Riemann theta functions, through observing asymptotic behaviours of the Baker-Akhiezer functions. We emphasize that we analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
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