S. Jin and X. Li. Multi-phase computations of the semi-classical limit of the Schrodinger equation and related problems. Physica D (in press), 2003. Home/Search Document Details and Download
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Wigner Functions versus WKB-Methods in Multivalued.. - Sparber, Markowich.. (2003) (Correct)
.... solution is accomplished using geometrical techniques of singularity theory and contact geometry (see e.g. Ar] AVG] Du] GuSt] A considerable amount of work has been done in recent years on constructing numerically the multivalued phase function (see, e.g. Be1] Be2] BKM] Ru] [JiLi]) We will not cover the arising numerical questions in this paper, instead we refer the interested reader to these references. In the last decade the use of Wigner functions and Wigner measures has drawn increasing interest, in particular its application to the semiclassical limit of Schrodinger ....
....of w in general is not closed. However, in geometrical optics, the multivalued form of the Wigner measure (for a fixed N) gives a closing condition which allows (in principle) the correct description of multivalued situations until the next caustic forms. For details on this problem (in d = 1) see [JiLi] and for some alternative approaches we refer to [Be1] Be2] Ru] 4.3 Concentration e#ects We now describe the behavior of the density at focal points, which typically arise as the onset of caustics. We will be able to distinguish between two specific cases of energy concentrations. Theorem ....
S. Jin, X. Li, Multiphase computation of the semiclassical limit of the Schrodinger equation and related problems, preprint Univ. of Wisconsin
A Level Set Method for the Computation of Multivalued Solutions .. - Jin, Osher (2003) (4 citations) Self-citation (Jin) (Correct)
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S. Jin, X.T. Li, Multi-phase computations of the semiclassical limit of the Schrodinger equation and related problems: Whitham vs. Wigner, Physica D, submitted.
A Level Set Method for Three-dimensional Paraxial.. - Shingyu Leung Jianliang (Correct)
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S. Jin and X. Li. Multi-phase computations of the semi-classical limit of the Schrodinger equation and related problems. Physica D (in press), 2003.
A Local Level Set Method for Paraxial Geometrical - Optics Jianliang Qian (Correct)
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S. Jin and X. Li. Multi-phase computations of the semi-classical limit of the Schrodinger equation and related problems. Physica D (in press), 2003.
Multiphase Semiclassical Approximation of an Electron in a.. - Gosse, Markowich (2003) (1 citation) (Correct)
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Shi Jin & X. Li, Multi-phase computations of the semiclassical limit of the Schrodinger equation and related problems: Whitham vs. Wigner, Physica D (to appear).
A Level Set Based Eulerian Method for Paraxial - Multivalued Traveltimes.. (Correct)
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S. Jin and X. Li. Multi-phase computations of the semi-classical limit of the Schrodinger equation and related problems. Physica D (in press), 2003.
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