Direct and inverse scattering problems of the nonlinear intermediate long wave equation

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  • Y. Kodama
    Bell Laboratories, Murray Hill, New Jersey 07974
  • M. J. Ablowitz
    Department of Mathematics, Clarkson College, Potsdam, New York 13676
  • J. Satsuma
    Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, Kyoto, Japan

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<jats:p>The inverse scattering transformation method associated with a nonlinear singular integrodifferential equation is discussed. The equation describes long internal gravity waves in a stratified fluid of finite depth, and reduces to the Korteweg–de Vries equation as shallow water limit and the Benjamin–Ono equation as deep water limit. Both limits of the method and novel aspects of the theory are also discussed.</jats:p>

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