3 citations · 3 across the 2 of their papers we have counts for
7 papers
The solution to the initial value problem for the ultradiscrete Somos-4 and 5 equations
Yoichi Nakata
We propose a method to solve the initial value problem for the ultradiscrete Somos-4 and Somos-5 equations by expressing terms in the equations as convex polygons and regarding max…
Periodic orbit analysis for the deterministic path-preference traffic flow cellular automaton
Yoichi Nakata, Yoshihiro Ohta, Sigeo Ihara
The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains…
Solutions to the ultradiscrete KP hierarchy and its reductions
Yoichi Nakata
We propose a recursive representation of solutions to an ultradiscrete analogue of the discrete KP hierarchy, which is the master equation of discrete soliton equations. We also pr…
Solutions to the ultradiscrete KdV equation expressed as the maximum of a quadratic function
Yoichi Nakata
We propose the functions defined by the maximum of a discrete quadratic form and satisfying the ultradiscrete KdV equation. These functions includes not only soliton solutions but…
Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs
Yoichi Nakata
We define a function by means of the minimum weight flow on a planar graph and prove that this function solves the ultradiscrete Toda molecule equation, its Bäcklund transformation…
Vertex operator for the non-autonomous ultradiscrete KP equation
Yoichi Nakata
We propose an ultradiscrete analogue of the vertex operator in the case of the ultradiscrete KP equation--several other ultradiscrete equations--which maps N-soliton solutions to N…