Inverse Scattering for the Nonlinear Schrödinger Equation with Cubic Convolution Nonlinearity

WATANABE, Michiyuki

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 59-67 / Harvested from Project Euclid

Résumé

In this paper it will be shown that a potential $V(x)$ and a constant $\lambda$ are uniquely determined from the scattering operator $S$ associated with the nonlinear Schrödinger equation \[ i\frac{\partial u}{\partial t}+(-\Delta+V)u+\lambda(|x|^{-\sigma}*|u|^{2})u=0 , \] and the corresponding unperturbed equation \[ i\frac{\partial u}{\partial t}-\Delta u=0 . \]

Publié le : 2001-06-15
Classification:

@article{1255958311,
     author = {WATANABE, Michiyuki},
     title = {Inverse Scattering for the Nonlinear Schr\"odinger Equation with Cubic Convolution Nonlinearity},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 59-67},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958311}
}

WATANABE, Michiyuki. Inverse Scattering for the Nonlinear Schrödinger Equation with Cubic Convolution Nonlinearity. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  59-67. http://gdmltest.u-ga.fr/item/1255958311/