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Kenta Nakata

Publications and source records attributed to Kenta Nakata.

5 recordsLinked to original sources
arXiv2025

Construction of the Lax pairs for the delay Lotka-Volterra and delay Toda lattice equations and their reductions to delay Painleve equations

The delay Lotka-Volterra and delay Toda lattice equations are delay-differential extensions of the well-known soliton equations, the Lotka-Volterra and Toda lattice equations, respectively. This paper investigates integrable properties of the delay Lotka-Volterra and delay Toda lattice equations, and study the relationships to the already known delay Painleve equations. First, Backlund transformations, Lax pairs and an infinite number of conserved quantities of these delay soliton equations are constructed. Then, applying spatial 2-periodic reductions to them, we show the known delay Painleve equations are derived. Using these reductions, we construct the N-soliton-type determinant solutions of the autonomous versions of delay Painleve equations, and the Casorati determinant solution of a higher order analogue of the discrete Painleve II equation.

nlin.SI↗
arXiv2024

A delay analogue of the box and ball system arising from the ultra-discretization of the delay discrete Lotka-Volterra equation

A delay analogue of the box and ball system (BBS) is presented. This new soliton cellular automaton is constructed by the ultra-discretization of the delay discrete Lotka-Volterra equation, which is an integrable delay analogue of the discrete Lotka-Volterra equation. Soliton patterns generated by this delay BBS are classified into normal solitons and abnormal solitons. Normal solitons have a clear relationship to the solitons of the BBS with K kinds of balls. On the other hand, abnormal solitons show various types of novel soliton patterns, which have not been observed in almost all known BBSs. We obtain them by numerical experiments, and then construct τ-functions of them analytically in 1-soliton cases.

nlin.SI↗
arXiv2022

Integrable delay-difference and delay-differential analogues of the KdV, Boussinesq, and KP equations

Delay-difference and delay-differential analogues of the KdV and Boussinesq (BSQ) equations are presented. Each of them has the N-soliton solution and reduces to an already known soliton equation as the delay parameter approaches 0. In addition, a delay-differential analogue of the KP equation is proposed. We discuss its N-soliton solution and the limit as the delay parameter approaches 0. Finally, the relationship between the delay-differential analogues of the KdV, BSQ, and KP equations is clarified. Namely, reductions of the delay KP equation yield the delay KdV and delay BSQ equations.

nlin.SI↗
arXiv2022

A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations

We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra, Toda lattice, and sine-Gordon equations and their multi-soliton solutions. It is carried out by applying a reduction and delay-differential limit to the discrete KP or discrete two-dimensional Toda lattice equations. Each of the delay-difference and delay-differential equations has the N-soliton solution, which depends on the delay parameter and converges to an N-soliton solution of a known soliton equation as the delay parameter approaches 0.

nlin.SI↗