Blog
About

23
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Systematic method of generating new integrable systems via inverse Miura maps

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          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 Schroedinger (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.

          Related collections

          Most cited references 87

          • Record: found
          • Abstract: not found
          • Article: not found

          Method for Solving the Korteweg-deVries Equation

            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Integrals of nonlinear equations of evolution and solitary waves

               Peter D. Lax (1968)
                Bookmark

                Author and article information

                Journal
                11 December 2010
                2011-02-18
                Article
                10.1063/1.3563585
                1012.2458

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                OIQP-10-09
                J. Math. Phys. 52 (2011) 053503
                48 pages; The method and results were implicitly used in arXiv:nlin/0105053 and arXiv:0712.4373; (v2) added one paragraph on p.12, to appear in JMP Vol.52 (2011)
                nlin.SI math-ph math.AP math.MP math.SP

                Comments

                Comment on this article