Lamé wave equation

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11: Bibliography R

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Plane wave scattering by a conducting elliptic cylinder coated by a nonconfocal dielectric. IEEE Trans. Antennas and Propagation 39 (2), pp. 218–223.

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6th item.

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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.

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MathReview (J. Shmoys)

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§12.17.

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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.

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ISSN 0044-2267, Document, MathReview Entry, ZentralBlatt

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§29.20(ii).

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Some Applications of the Lamé Function Solutions of the Linearised Supersonic Flow Equations. Technical Reports and Memoranda Technical Report 2865, Aeronautical Research Council (Great Britain).

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Notes:

Reprinted by Her Majesty’s Stationery Office, London, 1962.

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MathReview (P. Germain)

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§29.19(ii).

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On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.

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ISBN 3-7643-6287-1, MathReview Entry, ZentralBlatt

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5th item.

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12: Bibliography J

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Simple-periodic and Non-periodic Lamé Functions. Mathematical Centre Tracts, No. 72, Mathematisch Centrum, Amsterdam.

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ISBN 90-6196-130-0, MathReview (V. P. Madan)

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§29.1, §29.1, §29.18(i), §29.19(i), §29.20(i), §29.20(i), §29.22(ii), §29.3(v), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29, Notations L, Notations L, Notations L, Notations L.

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The effect on Love waves of heterogeneity in the lower layer. Monthly Notices Roy. Astronom. Soc. Geophysical Supplement 2, pp. 101–111.

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ZentralBlatt

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§9.1.

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Differential equations and mathematical biology. Chapman & Hall/CRC Mathematical and Computational Biology Series, CRC Press, Boca Raton, FL.

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Second edition of Jones and Sleeman (2003)

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ISBN 978-1-4200-8357-6, MathReview Entry, ZentralBlatt

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Profile Brian D. Sleeman.

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Differential equations and mathematical biology. Chapman & Hall/CRC Mathematical Biology and Medicine Series, Chapman & Hall/CRC, Boca Raton, FL.

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A second edition was published in 2010.

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ISBN 1-58488-296-4, MathReview (Jian Hong Wu), ZentralBlatt

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D. S. Jones, M. J. Plank, and B. D. Sleeman (2010).

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Acoustic and Electromagnetic Waves. Oxford Science Publications, The Clarendon Press Oxford University Press, New York.

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ISBN 0-19-853365-9, MathReview (John A. DeSanto)

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§10.73(i).

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13: Bibliography H

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Two-dimensional periodic waves in shallow water. II. Asymmetric waves. J. Fluid Mech. 285, pp. 95–122.

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ISSN 0022-1120, Document, MathReview

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Figure 21.9.1, Figure 21.9.1, Figure 21.9.2, Figure 21.9.2, §21.9, Sidebar 21.SB1, Sidebar 21.SB2.

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Two-dimensional periodic waves in shallow water. J. Fluid Mech. 209, pp. 567–589.

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ISSN 0022-1120, Document, MathReview

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§21.9, Sidebar 21.SB2.

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Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.

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Document, MathReview (F. M. Arscott), ZentralBlatt

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§29.16.

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Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.

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§33.7.

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The eigenvalues of the angular spheroidal wave equation. Stud. Appl. Math. 66 (3), pp. 217–240.

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ISSN 0022-2526, MathReview, ZentralBlatt

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§30.9(iii).

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14: Bibliography M

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Die Laméschen Wellenfunktionen des Drehellipsoids. Forschungsbericht No. 1952 ZWB (German).

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Notes:

English translation: Lamé wave functions of the ellipsoid of revolution appeared as NACA Technical Memorandum No. 1224, 1949

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MathReview

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§30.9(iii).

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Precise Coulomb wave functions for a wide range of complex $\mathrm{\ell }$, $\eta$ and $z$ . Computer Physics Communications 176 (3), pp. 232–249.

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Notes:

C++ code. Maximum accuracy 10D

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Document, Code, ZentralBlatt

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1st item.

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Asymptotic approximations for prolate spheroidal wave functions. Studies in Appl. Math. 54 (4), pp. 315–349.

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MathReview (M. L. Mehta), ZentralBlatt

Referenced by:

§30.9(i).

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Diatomic molecules according to the wave mechanics. II: Vibrational levels. Phys. Rev., II. Ser. 34, pp. 57–64.

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ISSN 0031-899X, ZentralBlatt

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(18.39.16).

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On asymptotic expansions of ellipsoidal wave functions. Math. Nachr. 32, pp. 157–172.

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Document, MathReview (F. M. Arscott), ZentralBlatt

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§29.11, §29.7(ii).

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15: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

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§29.19(ii).

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Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

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Online edition, MathReview (F. Ursell), ZentralBlatt

Referenced by:

§11.12.

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Wave functions for large arguments by the amplitude-phase method. Phys. Rev. 52, pp. 1123–1127.

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Document, ZentralBlatt

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§33.5(ii).

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Linear and Nonlinear Waves. John Wiley & Sons, New York.

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Notes:

Reprinted in 1999.

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ISBN 0471359424, MathReview, ZentralBlatt

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§9.16.

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A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.

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Document, MathReview (T. B. Benjamin), ZentralBlatt

Referenced by:

§21.9.

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16: Bibliography B

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Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.

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§36.14(i), §9.16.

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Waves and Thom’s theorem. Advances in Physics 25 (1), pp. 1–26.

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§36.14(i).

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Singularities in Waves and Rays. In Les Houches Lecture Series Session XXXV, R. Balian, M. Kléman, and J.-P. Poirier (Eds.), Vol. 35, pp. 453–543.

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§36.14(i).

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Prolate angular spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 187–192.

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Prolate radial spheroidal wave functions. Comput. Phys. Comm. 30 (2), pp. 177–185.

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17: Bibliography L

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Lamé-Wangerin functions. Quart. J. Math., Oxford Ser. (2) 3, pp. 107–114.

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Document, MathReview (A. Erdélyi), ZentralBlatt

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§29.17(ii).

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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics. J. Math. Phys. 27 (5), pp. 1238–1265.

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ISSN 0022-2488, Document, MathReview (Basilis C. Xanthopoulos), ZentralBlatt

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§30.12, §31.17(ii).

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Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.

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Mathematica package for eigenvalues and solutions of the spheroidal wave equations

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Code(SpheroidF), Document

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2nd item, 3rd item.

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Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equations 162 (1), pp. 27–63.

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ISSN 0022-0396, Document, MathReview (John Albert), ZentralBlatt

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§22.19(iii).

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Deep water ship-waves. Phil. Mag. 9, pp. 733–757.

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ZentralBlatt

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§36.13.

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18: Bibliography D

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Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.

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MathReview (A. E. Danese), ZentralBlatt

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§31.12.

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The KP equation with quasiperiodic initial data. Phys. D 123 (1-4), pp. 123–152.

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Notes:

Nonlinear waves and solitons in physical systems (Los Alamos, NM, 1997)

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ISSN 0167-2789, Document, MathReview (Pavel Krejčí), ZentralBlatt

Referenced by:

§21.9.

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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Document

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§15.18.

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Lamé instantons. J. High Energy Phys. 2000 (1), pp. Paper 19, 8.

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Notes:

(electronic only, article id. JHEP01(2000)019, 8 pp.).

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ISSN 1029-8479, Document, MathReview, ZentralBlatt

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§22.11.

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Coulomb wave functions with complex values of the variable and the parameters. J. Math. Phys. 40 (12), pp. 6145–6166.

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ISSN 0022-2488, Document, MathReview (Raj Wilson), ZentralBlatt

Referenced by:

§33.13.

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