Watanabe, Michiyuki Inverse scattering of the nonlinear Schrödinger equation with cubic convolution nonlinearity. (English) Zbl 1005.35093 Tokyo J. Math. 24, No. 1, 59-67 (2001). Summary: It is shown that a potential \(V(x)\) and a constant \(\lambda\) are uniquely determined from the scattering operator \(S\) associated with the nonlinear Schrödinger equation \[ i{\partial u\over \partial t}+(-\Delta+ V)u+\lambda \bigl(|x|^{-\sigma}*|u|^2 \bigr)u=0, \] and the corresponding unperturbed equation \(i{\partial u\over \partial t}-\Delta u=0\). Cited in 12 Documents MSC: 35R30 Inverse problems for PDEs 81U40 Inverse scattering problems in quantum theory 35P25 Scattering theory for PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:uniqueness; potential; scattering operator; nonlinear Schrödinger equation × Cite Format Result Cite Review PDF Full Text: DOI