A characteristic of solutions obtained by the inverse scattering method is the existence of solitons, solutions resembling both particles and waves, which have no analogue for linear partial differential equations.
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Is positive see and for a detailed description of the spectrum associated to the isospectral problem, for the inverse scattering approach in the case of smooth solutions that decay at infinity.
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Trubowitz studies scattering theory ( some with Percy Deift, and inverse scattering theory ), integrable systems and their connection to algebraic geometry, mathematical theory of Fermi liquids in the statistical mechanics.
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Soliton equations are a class of partial differential equations which can be studied and solved by a method called the inverse scattering transform, which reduces the nonlinear PDEs to a linear inverse scattering problem.
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Soliton equations are a class of partial differential equations which can be studied and solved by a method called the inverse scattering transform, which reduces the nonlinear PDEs to a linear inverse scattering problem.
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In 2006 he received the Leroy P . Steele Prize with Martin Kruskal, Robert M . Miura and Clifford S . Gardner for his work on inverse scattering transformations in the theory of solitons.
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In mathematics, the "'quantum inverse scattering method "'is a method for solving L . D . Faddeev in about 1979 . This method led to the formulation of quantum groups.
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This led to the discovery of an inverse scattering method for that equation by M . J . Ablowitz, D . J . Kaup, A . C . Newell, and H . Segur ( AKNS ).
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The inverse scattering or inverse spectral problem associated to the Cauchy problem for 1 + 1 dimensional partial differential equations on the line, periodic problems, or even initial-boundary value problems, can be stated as Riemann Hilbert problems.
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He is known for contributions to laser light scattering, more specifically the physics of the inverse scattering problem and for commercializing analytical methods and instruments involving laser light scattering, which are widely used in academia, industry, and government.
