7 citations · 22 across the 14 of their papers we have counts for
13 papers · 1 filter
Exact solutions to SIR epidemic models via integrable discretization
Atsushi Nobe
An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discret…
Periodicity, linearizability and integrability in seed mutations of type
Atsushi Nobe, Junta Matsukidaira
In the network of seed mutations arising from a certain initial seed, an appropriate path emanating from the initial seed is intendedly chosen, noticing periodicity of the exchange…
A family of integrable and non-integrable difference equations arising from cluster algebras
Atsushi Nobe, Junta Matsukidaira
The one-parameter family of second order nonlinear difference equations each of which is given by is expl…
Generators of rank 2 cluster algebras of affine types via linearization of seed mutations
Atsushi Nobe
From the viewpoint of integrable systems on algebraic curves, we discuss linearization of birational maps arising from the seed mutations of types and , whic…
Birational maps conjugate to the rank 2 cluster mutations of affine types and their geometry
Atsushi Nobe
Mutations of the cluster variables generating the cluster algebra of type reduce to a two-dimensional discrete integrable system given by a quartic birational map. The…
Mutations of the cluster algebra of type and the periodic discrete Toda lattice
Atsushi Nobe
A direct connection between two sequences of points, one of which is generated by seed mutations in the cluster algebra of type and the other by time evolutions of the…
On the addition formula for the tropical Hesse pencil
Atsushi Nobe
We give the addition formula for the tropical Hesse pencil, which is the tropicalization of the Hesse pencil parametrized by the level-three theta functions, via those for the ultr…
A geometric realization of the ultradiscrete periodic Toda lattice via tropical plane curves
Atsushi Nobe
This is a review article on a tropical geometric realization of the ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is translated into an addition on the…
A geometric realization of the periodic discrete Toda lattice and its tropicalization
Atsushi Nobe
An explicit formula concerning curve intersections equivalent to the time evolution of the periodic discrete Toda lattice is presented. First, the time evolution is realized as a p…
Addition in Jacobians of tropical hyperelliptic curves
Atsushi Nobe
We show that there exists a surjection from the set of effective divisors of degree on a tropical curve of genus to its Jacobian by using a tropical version of the Riemann-…
The group law on the tropical Hesse pencil
Atsushi Nobe
We show that the addition of points on the tropical Hesse curve can be realized via the intersection with a tropical line. Then the addition formula for the tropical Hesse curve is…
A tropical analogue of the Hessian group
Atsushi Nobe
We investigate a tropical analogue of the Hessian group , the group of linear automorphisms acting on the Hesse pencil. Through the procedure of ultradiscretization, the g…
An ultradiscrete integrable map arising from a pair of tropical elliptic pencils
Atsushi Nobe
We present a tropical geometric description of a piecewise linear map whose invariant curve is a concave polygon. In contrast to convex polygons, a concave one is not directly rela…