Detecting integrability of discrete equations on multi-dimensional lattices

2017 Fiscal Year Final Research Report

• Project/Area Number: 16H06711
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Mase Takafumi 東京大学, 大学院数理科学研究科, 特任助教 (80780105)
• Project Period (FY): 2016-08-26 – 2018-03-31
• Keywords: 可積分系 / 離散可積分系 / 代数的エントロピー

Outline of Final Research Achievements

We studied the integrability of discrete equations on multi-dimensional lattices, by means of cancellation of factors. First, we extended the so-called coprimeness condition. As a result, it has become possible to apply the coprimeness condition to more equations than before. We also showed that the nonlinear form of an extended version of the discrete Toda equation possesses this property. Moreover, in the case of equations on one-dimensional lattices, we developed a method to verify the integrability only by means of singularity confinement. Using the theory of algebraic surfaces, we revealed the meaning of our method in the case of second-order mappings.

Free Research Field

数物系科学・数学