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

Kenta Nakata*, Ken Ichi Maruno

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 (TL), 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 TL 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.

Original languageEnglish
Article number335201
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number33
DOIs
Publication statusPublished - 2022 Aug 19

Keywords

  • delay-difference equations
  • delay-differential equations
  • integrable systems
  • multi-soliton solutions
  • soliton equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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