Generalized Gel'fand-Levitan Equation and Variational Relations of the Kaup-Newell Equation

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概要

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• The generalized Gel'fand-Levitan integral equation is derived for solving the inverse problem of Kaup-Newell eigenvalue problem, which makes it possible to solve the derivative nonlinear Schrodinger equation etc. by the inverse Fourier Spectral transform. By this integral equation we obtained the variation of potentials as a functional of that of scattering data. The inverse functional relation is also given by perturbing the Kaup-Newell equation as to potentials. For both functionals the contribution from the discrete spectrum is obtained and the completeness of squared eigenfunctions is naturally derived. These functional relations play the important role for studying the dynamical property and the perturbational technique related to the nonlinear evolution equations solved by the Kaup-Newell equation.

• 核融合科学研究所の論文

著者

• Kawata T.

  Research Information Center Institute Of Plasma Physics Nagoya University:faculty Of Engineering Toy

• Sakai J.

  Research Information Center, Institute of Plasma Physics, Nagoya University

関連論文

• Inverse Method for the Mixed Nonlinear Schrodinger Equation and Soliton Solutions
• Generalized Gel'fand-Levitan Equation and Variational Relations of the Kaup-Newell Equation

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