论文标题
孤子方程的可集成延迟差异和延迟差异类似物的系统构建
A systematic construction of integrable delay-difference and delay-differential analogues of soliton equations
论文作者
论文摘要
我们提出了一种系统的方法，用于构建已知的孤子方程（例如Lotka-Volterra，Toda lattice和Sine-Gordon方程及其多丝溶液）等已知孤子方程的可集成延迟差异和延迟分化类似物。它是通过对离散KP或离散的二维TODA晶格方程应用降低和延迟分别限制来执行的。每个延迟分化和延迟分化方程都有N-Soliton解决方案，该解决方案取决于延迟参数，并收敛到已知孤子方程的N-Soliton解决方案，因为延迟参数接近0。
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.
