Zurnal matematiceskoj fiziki analiza geometrii · 2015 · 13 citations · 21 references
Natural SciencesMathematicsPhysicsDifferential EquationsMathematical PhysicsTheoretical PhysicsInverse Problems In MechanicsScattering ProblemsScattering TheorySchrödinger EquationAsymptotic Scattering TheoryInverse ScatteringInverse Scattering TransformKorteweg - De Vries EquationOperatorsScattering Inverse Problems
We study the direct and inverse scattering problem for the one-dimensional Schrödinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to its asymptotics. Our results generalize all previous known results and are important for solving the Korteweg-de Vries equation via the inverse scattering transform.
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Howard H. Brown · Journal of the Franklin Institute · 1954 · 1.9K citations
Inverse scattering on the line
Percy Deift, Eugene Trubowitz · Communications on Pure and Applied Mathematics · 1979 · 924 citations