Fredholm Determinants and the Cauchy Problem of a Class of Nonlinear Evolution Equations
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概要
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The Marchenko equation for the Zakharov-Shabat operator is studied in the framework of the Fredholm theory and the solution, the Zakharov-Shabat potential, is presented by the Fredholm determinant and the first minors, which are composed of the kernel of the Marchenko equation. The evolution of the potential due to the evolution of the kernel is proved to produce the solution of the Cauchy problem for a class of nonlinear evolution equations including the nonlinear Schrodinger equation and the modified Korteweg-de Vries equation. In Hirota's formulation by bilinear forms we separate the general identity associated to the redundancy in the inverse scattering method for the Zakharov-Shabat operator and show that the formulation is valid also in cases containing ripples in addition to solitons.
- 理論物理学刊行会の論文
- 1987-08-25
著者
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Kato Yusuke
Department Of Applied Biological Chemistry Graduate School Of Agricultural And Life Sciences Univers
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Kato Yusuke
Department Of Engineering Mathematics Utsunomiya University
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KATO Yusuke
Department of Engineering Mathematics Faculty of Engineering, Utsunomiya University
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