ICTS:30043

Video URL

On the singularity patterns of the discrete and modified-discrete KdV

On the singularity patterns of the discrete and modified-discrete KdV

(2024). On the singularity patterns of the discrete and modified-discrete KdV. SciVideos. https://youtube.com/live/L3lZJq7XrEY

On the singularity patterns of the discrete and modified-discrete KdV. SciVideos, Oct. 27, 2024, https://youtube.com/live/L3lZJq7XrEY 

          @misc{ scivideos_ICTS:30043,
            doi = {},
            url = {https://youtube.com/live/L3lZJq7XrEY},
            author = {},
            keywords = {},
            language = {en},
            title = {On the singularity patterns of the discrete and modified-discrete KdV},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30043 see, \url{https://scivideos.org/icts-tifr/30043}}
          }
Thamizharasi Tamizhmani
Talk numberICTS:30043
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

We study the structure of singularities in the discrete Korteweg–deVries equation and its modified sibling. Four different types of singularities are identified. The first type corresponds to localised, ‘confined’, singularities. Two other types of singularities are of infinite extent and consist of oblique lines. The fourth type of singularity corresponds to horizontal strips where the product of the values on vertically adjacent points is equal to 1. Due to its orientation this singularity can, in fact, interact with the other types. This type of singularity was dubbed ‘taishi’. The taishi can interact with singularities of the other two families, giving rise to very rich and quite intricate singularity structures. Nonetheless, these interactions can be described in a compact way through the formulation of a symbolic representation of the dynamics. We give an interpretation of this symbolic representation in terms of a box & ball system related to the ultradiscrete KdV equation.