Generalized AKNS Class of the Nonlinear Evolution Equations and Its Trace Formula and Dynamical structures

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  • AKNS クラス ニ ゾクスル イッパンカサレタ ヒセンケイ ハッテン ホウテ
  • AKNSクラスに属する一般化された非線形発展方程式とそのトレース公式及び力学的な構造

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The generalized theory belonging to the AKNS class of nonlinear evolution equations is reviewed and some topics relating with dynamical natures are discussed rigorously. The general solvable class with a closed formula is given from directly solving its integrable conditions and from analysis of squared eigenstates. Conservbation laws are derived by using both trace method and squared eigenvalue problem. We naturally define a canonical equation of course equivalent to the generalized equation and the corresponding Poisson bracket. Each constant of motions are prooved to commute each other, then we show an existense of infinitesimal cannonical transformation which allows the system an infinite dimensional abelian symmetry corresponding to the "half" Kac-Moody Lie algebra. This representation directly connects to the infinite conservations of integrable nonlinear systems because of using a canonical frame.

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