-
2
-
-
84984525506
-
Computation of wave fields in inhomogeneous media-Gaussian beam approach
-
V. Červený, M. Popov, and I. Pšenč́k, Computation of wave fields in inhomogeneous media-Gaussian beam approach, Geophysics J. R. Astr. Soc., 70 (1982), pp. 109-128.
-
(1982)
Geophysics J. R. Astr. Soc.
, Issue.70
, pp. 109-128
-
-
Červený, V.1
Popov, M.2
Pšenč́k, I.3
-
3
-
-
3242697504
-
Computational high-frequency wave propagation using the level set method, with applications to the semi-classical limit of Schrödinger equations
-
L.-T. Cheng, H. Liu, and S. Osher, Computational high-frequency wave propagation using the level set method, with applications to the semi-classical limit of Schrödinger equations, Commun. Math. Sci., 1 (2003), pp. 593-621.
-
(2003)
Commun. Math. Sci.
, vol.1
, pp. 593-621
-
-
Cheng, L.-T.1
Liu, H.2
Osher, S.3
-
4
-
-
84967758647
-
Viscosity solutions of hamilton-jacobi equations
-
M. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), pp. 1-42.
-
(1983)
Trans. Amer. Math. Soc.
, vol.277
, pp. 1-42
-
-
Crandall, M.1
Lions, P.-L.2
-
5
-
-
24644487123
-
Computational high frequency wave propagation
-
B. Engquist and O. Runborg, Computational high frequency wave propagation, Acta Numer., 12 (2003), pp. 181-266.
-
(2003)
Acta Numer.
, vol.12
, pp. 181-266
-
-
Engquist, B.1
Runborg, O.2
-
6
-
-
0035387609
-
Prestack Gaussian-beam depth migration
-
N. Hill, Prestack Gaussian-beam depth migration, Geophys., 66 (2001), pp. 1240-1250.
-
(2001)
Geophys.
, vol.66
, pp. 1240-1250
-
-
Hill, N.1
-
7
-
-
0002820858
-
Fourier integral operator
-
L. Hörmander, Fourier integral operator, I, Acta. Math., 127 (1971), pp. 79-83.
-
(1971)
I, Acta. Math.
, Issue.127
, pp. 79-83
-
-
Hörmander, L.1
-
8
-
-
0002709344
-
On the existence and the regularity of solutions of linear pseudo-differential equations
-
L. Hörmander, On the existence and the regularity of solutions of linear pseudo-differential equations, Enseign. Math., 17 (1971), pp. 99-163.
-
(1971)
Enseign. Math.
, vol.17
, pp. 99-163
-
-
Hörmander, L.1
-
9
-
-
23944519965
-
Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems
-
S. Jin, H. Liu, S. Osher, and R. Tsai, Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, J. Comput. Phys., 210 (2005), pp. 497-518.
-
(2005)
J. Comput. Phys.
, vol.210
, pp. 497-518
-
-
Jin, S.1
Liu, H.2
Osher, S.3
Tsai, R.4
-
10
-
-
16844373042
-
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
-
S. Jin, H. Liu, S. Osher, and Y.-H. R. Tsai, Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation, J. Comput. Phys., 205 (2005), pp. 222-241.
-
(2005)
J. Comput. Phys.
, vol.205
, pp. 222-241
-
-
Jin, S.1
Liu, H.2
Osher, S.3
Tsai, Y.-H.R.4
-
11
-
-
3242673880
-
A level set method for the computation of multivalued solutions to quasilinear hyperbolic PDEs and Hamilton-Jacobi equations
-
S. Jin and S. Osher, A level set method for the computation of multivalued solutions to quasilinear hyperbolic PDEs and Hamilton-Jacobi equations, Commun. Math. Sci., 1 (2003), pp. 575-591.
-
(2003)
Commun. Math. Sci.
, vol.1
, pp. 575-591
-
-
Jin, S.1
Osher, S.2
-
12
-
-
77950364040
-
Gaussian beam methods for the Schrödinger equation in the semiclassical regime: Lagrangian and Eulerian formulations
-
S. Jin, H.Wu, and X. Yang, Gaussian beam methods for the Schrödinger equation in the semiclassical regime: Lagrangian and Eulerian formulations, Commun. Math. Sci., 6 (2008), pp. 995-1020.
-
(2008)
Commun. Math. Sci.
, vol.6
, pp. 995-1020
-
-
Jin, S.1
Wu, H.2
Yang, X.3
-
13
-
-
0000724502
-
Corrected Bohr-Sommerfeld quantum conditions for non-separable systems
-
J. Keller, Corrected Bohr-Sommerfeld quantum conditions for non-separable systems, Ann. Physics, 4 (1958), pp. 180-188.
-
(1958)
Ann. Physics
, vol.4
, pp. 180-188
-
-
Keller, J.1
-
14
-
-
61349126449
-
Eulerian Gaussian beams for Schrödinger equations in the semiclassical regime
-
S. Leung and J. Qian, Eulerian Gaussian beams for Schrödinger equations in the semiclassical regime, J. Comput. Phys., 228 (2009), pp. 2951-2977.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 2951-2977
-
-
Leung, S.1
Qian, J.2
-
15
-
-
34548534954
-
Eulerian Gaussian beams for high frequency wave propagation
-
S. Leung, J. Qian, and R. Burridge, Eulerian Gaussian beams for high frequency wave propagation, Geophys., 72 (2007), pp. 61-76.
-
(2007)
Geophys.
, vol.72
, pp. 61-76
-
-
Leung, S.1
Qian, J.2
Burridge, R.3
-
17
-
-
33845497473
-
A level set framework for capturing multi-valued solutions of nonlinear first-order equations
-
H. Liu, L.-T. Cheng, and S. Osher, A level set framework for capturing multi-valued solutions of nonlinear first-order equations, J. Sci. Comput., 29 (2006), pp. 353-373.
-
(2006)
J. Sci. Comput.
, vol.29
, pp. 353-373
-
-
Liu, H.1
Cheng, L.-T.2
Osher, S.3
-
18
-
-
34447280082
-
Multi-valued solution and level set methods in computational high frequency wave propagation
-
H. Liu, S. Osher, and Y.-H. R. Tsai, Multi-valued solution and level set methods in computational high frequency wave propagation, Comm. Comput. Phys., 1 (2006), pp. 765-804.
-
(2006)
Comm. Comput. Phys.
, vol.1
, pp. 765-804
-
-
Liu, H.1
Osher, S.2
Tsai, Y.-H.R.3
-
19
-
-
34447264074
-
A field-space-based level set method for computing multi-valued solutions to Euler-Poisson equations
-
H. Liu and Z. Wang, A field-space-based level set method for computing multi-valued solutions to Euler-Poisson equations, J. Comput. Phys., 225 (2007), pp. 591-614.
-
(2007)
J. Comput. Phys.
, vol.225
, pp. 591-614
-
-
Liu, H.1
Wang, Z.2
-
20
-
-
49749100791
-
Superposition of multi-valued solutions in high frequency wave dynamics
-
H. Liu and Z. Wang, Superposition of multi-valued solutions in high frequency wave dynamics, J. Sci. Comput., 35 (2008), pp. 192-218.
-
(2008)
J. Sci. Comput.
, vol.35
, pp. 192-218
-
-
Liu, H.1
Wang, Z.2
-
21
-
-
62049085150
-
A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations
-
H. Liu and Z. Wang, A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations, J. Comput. Phys., 228 (2009), pp. 3326-3344.
-
(2009)
J. Comput. Phys.
, vol.228
, pp. 3326-3344
-
-
Liu, H.1
Wang, Z.2
-
22
-
-
36449006348
-
A Wigner-function approach to (semi)-classical limits: Electrons in a periodic potential
-
P. A. Markowich, N. J. Mauser, and F. Poupaud, A Wigner-function approach to (semi)-classical limits: Electrons in a periodic potential, J. Math. Phys., 35 (1994), pp. 1066-1094.
-
(1994)
J. Math. Phys.
, vol.35
, pp. 1066-1094
-
-
Markowich, P.A.1
Mauser, N.J.2
Poupaud, F.3
-
23
-
-
0039223379
-
Weak limits of finite difference schemes of Schrödinger-type equations
-
P. Markowich, P. Pietra, and C. Pohl, Weak limits of finite difference schemes of Schrödinger-type equations, Pybbl. Ian., 1035 (1997), pp. 1-57.
-
(1997)
Pybbl. Ian.
, vol.1035
, pp. 1-57
-
-
Markowich, P.1
Pietra, P.2
Pohl, C.3
-
24
-
-
1842557759
-
Semiclassical approximation in quantum mechanics
-
D. Reidel, Dordrecht, The Netherlands
-
V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics, Math. Phys. Appl. Math. 7, D. Reidel, Dordrecht, The Netherlands, 1981.
-
(1981)
Math. Phys. Appl. Math.
, vol.7
-
-
Maslov, V.P.1
Fedoriuk, M.V.2
-
26
-
-
0036647932
-
Geometric optics in a phasespace-based level set and eulerian framework
-
S. Osher, L.-T. Cheng, M. Kang, H. Shim, and Y.-H. Tsai, Geometric optics in a phasespace-based level set and Eulerian framework, J. Comput. Phys., 179 (2002), pp. 622-648.
-
(2002)
J. Comput. Phys.
, vol.179
, pp. 622-648
-
-
Osher, S.1
Cheng, L.-T.2
Kang, M.3
Shim, H.4
Tsai, Y.-H.5
-
27
-
-
3242656105
-
A level set based Eulerian method for paraxial multivalued traveltimes
-
J. Qian and S. Leung, A level set based Eulerian method for paraxial multivalued traveltimes, J. Comput. Phys., 197 (2004), pp. 711-736.
-
(2004)
J. Comput. Phys.
, vol.197
, pp. 711-736
-
-
Qian, J.1
Leung, S.2
-
28
-
-
0000952462
-
Gaussian beams and the propagation of singularities, in Studies in Partial Differential Equations
-
Math. Assoc. America, Washington, DC
-
J. Ralston, Gaussian beams and the propagation of singularities, in Studies in Partial Differential Equations, MAA Stud. Math. 23, Math. Assoc. America, Washington, DC, 1982.
-
(1982)
MAA Stud. Math.
, vol.23
-
-
Ralston, J.1
-
29
-
-
77956050864
-
-
available online from
-
J. Ralston, Gaussian Beams, 2005; available online from http://www.math.ucla.edu/ralston/pub/Gaussnotes.pdf.
-
(2005)
Gaussian Beams
-
-
Ralston, J.1
-
30
-
-
35349007284
-
Mathematical models and numerical methods for high frequency waves
-
O. Runborg, Mathematical models and numerical methods for high frequency waves, Commun. Comput. Phys., 2 (2007), pp. 827-880.
-
(2007)
Commun. Comput. Phys.
, vol.2
, pp. 827-880
-
-
Runborg, O.1
-
31
-
-
84887251437
-
Multivalued geometrical optics: Wigner functions versus WKB-methods
-
C. Sparber, P. Markowich, and N. J. Mauser, Multivalued geometrical optics: Wigner functions versus WKB-methods, Asymptot. Anal., 33 (2003), pp. 153-187.
-
(2003)
Asymptot. Anal.
, vol.33
, pp. 153-187
-
-
Sparber, C.1
Markowich, P.2
Mauser, N.J.3
-
32
-
-
45849084964
-
Mountain waves and Gaussian beams
-
N. M. Tanushev, J. Qian, and J. V. Ralston, Mountain waves and Gaussian beams, Multiscale Model. Simul., 6 (2007), pp. 688-709.
-
(2007)
Multiscale Model. Simul.
, vol.6
, pp. 688-709
-
-
Tanushev, N.M.1
Qian, J.2
Ralston, J.V.3
-
33
-
-
49349099865
-
Superpositions and higher order Gaussian beams
-
N. M. Tanushev, Superpositions and higher order Gaussian beams, Commun. Math. Sci., 6 (2008), pp. 449-475.
-
(2008)
Commun. Math. Sci.
, vol.6
, pp. 449-475
-
-
Tanushev, N.M.1
-
34
-
-
33745014742
-
On the quantum correction for thermodynamic equilibrium
-
E. P. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev., 40 (1932), pp. 749-759.
-
(1932)
Phys. Rev.
, vol.40
, pp. 749-759
-
-
Wigner, E.P.1
|