Ultradiscrete permanent solution to the ultradiscrete Kadomtsev–Petviashvili equation

  • Hidetomo NagaiEmail author
Original Paper Area 1


We propose an ultradiscrete permanent solution to the ultradiscrete Kadomtsev–Petviashvili (KP) equation. The ultradiscrete permanent is an ultradiscrete analogue of the usual permanent. The elements on this ultradiscrete permanent solution are required some additional relations other than the ultradiscrete dispersion relation. We confirm the solution satisfying these relations and propose some explicit examples of the solution.


Soliton equation Ultradiscrete system Kadomtsev–Petviashvili equation Ultradiscrete Permanent 

Mathematics Subject Classification

35C08 39C08 



The author is grateful to Professor Daisuke Takahashi for helpful advice. The author also grateful Keisuke Mizuki for valuable discussions.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTokai UniversityHiratsukaJapan

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