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1974•Progress of Theoretical PhysicsOpen access

On the Extension of Inverse Scattering Method

Miki Wadati, Toshio Kamijo

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Abstract

The inverse scattering method is extended into n×n matrix form so as to include wider classes of nonlinear differential equations. As a mathematical foundation for the extension, the inverse scattering problem for n×n Schrödinger equation is discussed and Gelfand-Levitan-Marchenko equation for the system is derived. Some of the applications of the theory are also discussed.

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What this paper is about

The inverse scattering method is extended into n×n matrix form so as to include wider classes of nonlinear differential equations. As a mathematical foundation for the extension, the inverse scattering problem for n×n Schrödinger equation is discussed and Gelfand-Levitan-Marchenko equation for the system is derived. Some of the applications of the theory are also discussed.

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OpenAlex reports 116 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The inverse scattering method is extended into n×n matrix form so as to include wider classes of nonlinear differential equations. As a mathematical foundation for the extension, the inverse scattering problem for n×n Schrödinger equation is discussed and Gelfand-Levitan-Marchenko equation for the system is derived. Some of the applications of the theory are also discussed.

Key concepts: Inverse scattering transform, Quantum inverse scattering method, Physics, Inverse scattering problem, Extension (predicate logic), Scattering, Scattering theory, Inverse

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