A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations
arXiv:2201.09474 · doi:10.1088/1751-8121/ac7f07
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, 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.
arXiv comment15 pages
References in corpus (11)
- Solvable Optimal Velocity Models and Asymptotic Trajectory
- Casorati Determinant Solution for the Relativistic Toda Lattice Equation
- Bilinearization of Discrete Soliton Equations and Singularity Confinement
- Algebraic entropy for differential-delay equations
- Singularity confinement in delay-differential Painlevé equations
- Special Solutions of Bi-Riccati Delay-Differential Equations
- Exact shock solution of a coupled system of delay differential equations: a car-following model
- Direct delay reductions of the Toda hierarchy
- Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
- A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system
- Delay reductions of the two-dimensional Toda lattice equation