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Trasformata inversa di scattering Inverse scattering transform Inverse Streutransformation
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In matematica, la trasformata inversa di scattering è un metodo per risolvere alcune equazioni alle derivate parziali non lineari. Può essere visto come un analogo non lineare, e in un certo senso una generalizzazione, della trasformata di Fourier, che viene ampiamente usata per risolvere molte equazioni alle derivate parziali lineari. Il nome "trasformata inversa di scattering" deriva dall'idea chiave di ricavare l'evoluzione temporale di un potenziale dall'evoluzione temporale dei suoi dati di scattering: lo scattering inverso si riferisce al problema di ricavare un potenziale di interazione partendo dalla matrice di scattering, in contrapposizione al problema di scattering diretto, in cui si calcola la matrice di scattering conoscendo il potenziale. Die Inverse Streutransformation (englisch Inverse Scattering Transformation, kurz IST) ist ein Verfahren zur exakten Lösung von Anfangswertproblemen bestimmter nichtlinearer partieller Differentialgleichungen (Evolutionsgleichungen) wie der Korteweg-de-Vries-Gleichung (KdV), die Solitonen beschreiben. In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential equations. The method is a non-linear analogue, and in some sense generalization, of the Fourier transform, which itself is applied to solve many linear partial differential equations. The name "inverse scattering method" comes from the key idea of recovering the time evolution of a potential from the time evolution of its scattering data: inverse scattering refers to the problem of recovering a potential from its scattering matrix, as opposed to the direct scattering problem of finding the scattering matrix from the potential.
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Martin D. Robert M. John M. Clifford S.
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Kruskal Miura Greene Gardner
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1974 1967
dbo:abstract
In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential equations. The method is a non-linear analogue, and in some sense generalization, of the Fourier transform, which itself is applied to solve many linear partial differential equations. The name "inverse scattering method" comes from the key idea of recovering the time evolution of a potential from the time evolution of its scattering data: inverse scattering refers to the problem of recovering a potential from its scattering matrix, as opposed to the direct scattering problem of finding the scattering matrix from the potential. The inverse scattering transform may be applied to many of the so-called exactly solvable models, that is to say completely integrable infinite dimensional systems. Die Inverse Streutransformation (englisch Inverse Scattering Transformation, kurz IST) ist ein Verfahren zur exakten Lösung von Anfangswertproblemen bestimmter nichtlinearer partieller Differentialgleichungen (Evolutionsgleichungen) wie der Korteweg-de-Vries-Gleichung (KdV), die Solitonen beschreiben. In matematica, la trasformata inversa di scattering è un metodo per risolvere alcune equazioni alle derivate parziali non lineari. Può essere visto come un analogo non lineare, e in un certo senso una generalizzazione, della trasformata di Fourier, che viene ampiamente usata per risolvere molte equazioni alle derivate parziali lineari. Il nome "trasformata inversa di scattering" deriva dall'idea chiave di ricavare l'evoluzione temporale di un potenziale dall'evoluzione temporale dei suoi dati di scattering: lo scattering inverso si riferisce al problema di ricavare un potenziale di interazione partendo dalla matrice di scattering, in contrapposizione al problema di scattering diretto, in cui si calcola la matrice di scattering conoscendo il potenziale. La trasformata inversa di scattering può essere applicata a molti dei cosiddetti modelli esattamente risolvibili, vale a dire sistemi completamente integrabili con uno spazio delle soluzioni a infinite dimensioni.
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