Discrete Crum’s Theorems and Lattice KdV-Type Equations

Cheng Zhang, Linyu Peng, Da jun Zhang

研究成果: Article

抜粋

We develop Darboux transformations (DTs) and their associated Crum’s formulas for two Schrödinger-type difference equations that are themselves discretized versions of the spectral problems of the KdV and modified KdV equations. With DTs viewed as a discretization process, classes of semidiscrete and fully discrete KdV-type systems, including the lattice versions of the potential KdV, potential modified KdV, and Schwarzian KdV equations, arise as the consistency condition for the differential/difference spectral problems and their DTs. The integrability of the underlying lattice models, such as Lax pairs, multidimensional consistency, τ-functions, and soliton solutions, can be easily obtained by directly applying the discrete Crum’s formulas.

元の言語English
ページ(範囲)165-182
ページ数18
ジャーナルTheoretical and Mathematical Physics(Russian Federation)
202
発行部数2
DOI
出版物ステータスPublished - 2020 2 1
外部発表Yes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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