Box-basket-ball systems

Thomas Lam, Pavlo Pylyavskyy, Reiho Sakamoto

Research output: Contribution to journalReview articlepeer-review


Using the whurl relation of the first two authors, we define a new discrete solitonic system, which we call the box-basket-ball system, generalizing the box-ball system of Takahashi and Satsuma. In box-basket-ball systems, balls may be put either into boxes or into baskets. While boxes stay fixed, both balls and baskets get moved during time evolution. Balls and baskets behave as fermionic and bosonic particles, respectively. We classify the solitons of this system, and study their scattering.

Original languageEnglish (US)
Article number1250019
JournalReviews in Mathematical Physics
Issue number8
StatePublished - Sep 2012

Bibliographical note

Funding Information:
T. L. is supported by NSF grant DMS-0901111, and by a Sloan Fellowship. P. P. was supported by NSF grant DMS-0757165. R. S. is partially supported by Grants-in-Aid for Scientific Research No. 21740114 from JSPS.


  • Box-ball system
  • discrete solitonic system
  • whurl relation


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