2011年5月
Systematic method of generating new integrable systems via inverse Miura maps
JOURNAL OF MATHEMATICAL PHYSICS
- 巻
- 52
- 号
- 5
- 開始ページ
- 053503
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.1063/1.3563585
- 出版者・発行元
- AMER INST PHYSICS
We provide a new natural interpretation of the Lax representation for an integrable system; that is, the spectral problem is the linearized form of a Miura transformation between the original system and a modified version of it. On the basis of this interpretation, we formulate a systematic method of identifying modified integrable systems that can be mapped to a given integrable system by Miura transformations. Thus, this method can be used to generate new integrable systems from known systems through inverse Miura maps; it can be applied to both continuous and discrete systems in 1 + 1 dimensions as well as in 2 + 1 dimensions. The effectiveness of the method is illustrated using examples such as the nonlinear Schrodinger (NLS) system, the Zakharov-Ito system (two-component KdV), the three-wave interaction system, the Yajima-Oikawa system, the Ablowitz-Ladik lattice (integrable space-discrete NLS), and two (2 + 1)-dimensional NLS systems. (C) 2011 American Institute of Physics. [doi:10.1063/1.3563585]
- リンク情報
- ID情報
-
- DOI : 10.1063/1.3563585
- ISSN : 0022-2488
- Web of Science ID : WOS:000291106000028