2020年2月1日
Discrete Crum’s Theorems and Lattice KdV-Type Equations
Theoretical and Mathematical Physics(Russian Federation)
- ,
- ,
- 巻
- 202
- 号
- 2
- 開始ページ
- 165
- 終了ページ
- 182
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1134/S0040577920020038
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.
- リンク情報
- ID情報
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- DOI : 10.1134/S0040577920020038
- ISSN : 0040-5779
- eISSN : 1573-9333
- ORCIDのPut Code : 71949907
- SCOPUS ID : 85083275266