Integrable boundary conditions for the Hirota-Miwa equation and Lie\n algebras

2019/06/14 by I. T. Habibullin, Habibullin, Ismagil, A R Khakimova +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1906.06063

openalex publication_date 2019/06/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Systems of discrete equations on a quadrilateral graph related to the series\nD⁽²⁾_N of the affine Lie algebras are studied. The systems are derived\nfrom the Hirota-Miwa equation by imposing boundary conditions compatible with\nthe integrability property. The Lax pairs for the systems are presented. It is\nshown that in the continuum limit the quad systems tend to the corresponding\nsystems of the differential equations belonging to the well-know\nDrinfeld-Sokolov hierarchies. The problem of finding the formal asymptotic\nexpansion of the solutions to the Lax equations is studied. Generating\nfunctions for the local conservation laws are found for the systems\ncorresponding to D⁽²⁾₃. An example of the higher symmetry is presented.\n

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