Systematic method of generating new integrable systems via inverse Miura maps

摘要

We provide a new natural interpretation of the Lax representation for anintegrable system; that is, the spectral problem is the linearized form of aMiura transformation between the original system and a modified version of it.On the basis of this interpretation, we formulate a systematic method ofidentifying modified integrable systems that can be mapped to a givenintegrable system by Miura transformations. Thus, this method can be used togenerate new integrable systems from known systems through inverse Miura maps;it can be applied to both continuous and discrete systems in 1+1 dimensions aswell as in 2+1 dimensions. The effectiveness of the method is illustrated usingexamples such as the nonlinear Schroedinger (NLS) system, the Zakharov-Itosystem (two-component KdV), the three-wave interaction system, theYajima-Oikawa system, the Ablowitz-Ladik lattice (integrable space-discreteNLS), and two (2+1)-dimensional NLS systems.