Direct and inverse scattering for nonlinear Schrödinger equation in 2D

DOI10.1063/1.4769825zbMath1331.35145OpenAlexW2045804147MaRDI QIDQ2872449

Markus Harju, Georgios Fotopoulos, Valery Serov

Publication date: 14 January 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4769825

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (10)

Solvability of a non-linear Cauchy problem for an elliptic equation ⋮ Inverse fixed energy scattering problem for the two-dimensional nonlinear Schrödinger operator ⋮ Inverse medium scattering for a nonlinear Helmholtz equation ⋮ The direct and inverse scattering problem for the semilinear Schrödinger equation ⋮ Inverse scattering for three-dimensional quasi-linear biharmonic operator ⋮ Reconstruction of singularities in two-dimensional quasi-linear biharmonic operator ⋮ Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line ⋮ Inverse scattering with fixed observation angle data in 2D ⋮ Two-dimensional inverse scattering for quasi-linear biharmonic operator ⋮ Numerical results for Saito’s uniqueness theorem in inverse scattering theory

Cites Work

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• Explicit characterization of the support of non-linear inclusions
• Applied functional analysis. Applications to mathematical physics. Vol. 1
• New mapping properties for the resolvent of the Laplacian and recovery of singularities of a multi-dimensional scattering potential
• A uniqueness theorem and reconstruction of singularities for a two-dimensional nonlinear Schrödinger equation
• Inverse backscattering problem for the generalized nonlinear Schrödinger operator in two dimensions
• INVERSE BORN APPROXIMATION FOR THE GENERALIZED NONLINEAR SCHRÖDINGER OPERATOR IN TWO DIMENSIONS
• An inverse Born approximation for the general nonlinear Schrödinger operator on the line
• Global uniqueness for a semilinear elliptic inverse problem
• Inverse Born approximation for the nonlinear two-dimensional Schrödinger operator

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