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Journal articles on the topic 'Lamé equation'

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Published: 4 June 2025

Last updated: 15 July 2025

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1

Reiter, Stefan. "Halphen's transform and middle convolution." Journal für die reine und angewandte Mathematik (Crelles Journal) 2015, no. 704 (2015): 1–20. http://dx.doi.org/10.1515/crelle-2013-0048.

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AbstractWe show that the Halphen transform of a Lamé equation can be written as the symmetric square of the Lamé equation followed by an Euler transform. We use this to compute a list of Lamé equations with arithmetic Fuchsian monodromy group. It contains all those Lamé equations where the quaternion algebra

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2

Maier, Robert S. "Lamé polynomials, hyperelliptic reductions and Lamé band structure." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1867 (2007): 1115–53. http://dx.doi.org/10.1098/rsta.2007.2063.

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The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter ℓ , the dispersion relation is reduced to the ℓ =1 dispersion relation, and a previously published ℓ =2 dispersion relation is shown to be partly incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solutions in terms of ℓ =1 solutions, is the chief tool. It is based on a projection from a genus- ℓ hyperelliptic curve, which parametrizes solutions, to an elliptic curve. A general formula for this covering is

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3

Fedoryuk, M. V. "The Lamé wave equation." Russian Mathematical Surveys 44, no. 1 (1989): 153–80. http://dx.doi.org/10.1070/rm1989v044n01abeh002009.

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4

Babich, E. R., and I. P. Martynov. "On the absence of logarithmic singularities in the solutions of Lamé-type equations." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 4 (2021): 428–34. http://dx.doi.org/10.29235/1561-2430-2021-57-4-428-434.

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The object of this research is linear differential equations of the second order with regular singularities. We extend the concept of a regular singularity to linear partial differential equations. The general solution of a linear differential equation with a regular singularity is a linear combination of two linearly independent solutions, one of which in the general case contains a logarithmic singularity. The well-known Lamé equation, where the Weierstrass elliptic function is one of the coefficients, has only meromorphic solutions. We consider such linear differential equations of the seco

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5

Ohmiya, Mayumi. "Darboux-Lamé equation and isomonodromic deformation." Abstract and Applied Analysis 2004, no. 6 (2004): 511–24. http://dx.doi.org/10.1155/s108533750430309x.

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The Darboux-Lamé equation is defined as the double Darboux transformation of the Lamé equation, and is studied from the viewpoint of the isomonodromic deformation theory. It is shown that the second-order ordinary differential equation of Fuchsian type onP1correspondingto the second Darboux-Lamé equation is obtained as isomonodromic deformation of some specific Gauss' hypergeometric differential equation.

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6

Dassios, George, and George Fragoyiannis. "Analytical Computation of Hyper-Ellipsoidal Harmonics." Mathematics 12, no. 15 (2024): 2433. http://dx.doi.org/10.3390/math12152433.

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The four-dimensional ellipsoid of an anisotropic hyper-structure corresponds to the four-dimensional sphere of an isotropic hyper-structure. In three dimensions, both theories for spherical and ellipsoidal harmonics have been developed by Laplace and Lamé, respectively. Nevertheless, in four dimensions, only the theory of hyper-spherical harmonics is hitherto known. This void in the literature is expected to be filled up by the present work. In fact, it is well known that the spectral decomposition of the Laplace equation in three-dimensional ellipsoidal geometry leads to the Lamé equation. Th

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7

Schief, W. K., A. Szereszewski, and C. Rogers. "The Lamé equation in shell membrane theory." Journal of Mathematical Physics 48, no. 7 (2007): 073510. http://dx.doi.org/10.1063/1.2747721.

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8

Chen, Zhijie, Ting-Jung Kuo, and Chang-Shou Lin. "The geometry of generalized Lamé equation, I." Journal de Mathématiques Pures et Appliquées 127 (July 2019): 89–120. http://dx.doi.org/10.1016/j.matpur.2018.08.004.

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9

Tajima, S. "Perturbed Lamé equation and the Buslaev phase." Ukrainian Mathematical Journal 50, no. 12 (1998): 1908–16. http://dx.doi.org/10.1007/bf02514206.

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10

Maier, Robert S. "Algebraic solutions of the Lamé equation, revisited." Journal of Differential Equations 198, no. 1 (2004): 16–34. http://dx.doi.org/10.1016/j.jde.2003.06.006.

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11

Cheng, Guangsen, Xingyao Yin, and Zhaoyun Zong. "Nonlinear amplitude-variation-with-offset inversion for Lamé parameters using a direct inversion method." Interpretation 5, no. 3 (2017): SL57—SL67. http://dx.doi.org/10.1190/int-2016-0168.1.

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Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear

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12

Correa, Francisco, Luis-Miguel Nieto, and Mikhail S. Plyushchay. "Hidden nonlinear supersymmetry of finite-gap Lamé equation." Physics Letters B 644, no. 1 (2007): 94–98. http://dx.doi.org/10.1016/j.physletb.2006.11.020.

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13

Brihaye, Y., and M. Godart. "Quasi exactly solvable extensions of the Lamé equation." Journal of Mathematical Physics 34, no. 11 (1993): 5283–91. http://dx.doi.org/10.1063/1.530304.

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14

Bazhanov, Vladimir V., and Vladimir V. Mangazeev. "Eight-vertex model and non-stationary Lamé equation." Journal of Physics A: Mathematical and General 38, no. 8 (2005): L145—L153. http://dx.doi.org/10.1088/0305-4470/38/8/l01.

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15

Kasperczuk, S. P. "Integrability of Hamiltonian systems and the Lamé equation." Applied Mathematics Letters 18, no. 5 (2005): 555–61. http://dx.doi.org/10.1016/j.aml.2004.03.019.

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16

Grosset, M. P., and A. P. Veselov. "Lamé Equation, Quantum Euler Top and Elliptic Bernoulli Polynomials." Proceedings of the Edinburgh Mathematical Society 51, no. 3 (2008): 635–50. http://dx.doi.org/10.1017/s0013091505001872.

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AbstractA generalization of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied in order to compute the coefficients of the spectral polynomials for the classical Lamé operator.

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17

GANGULY, ASISH. "ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ)". Modern Physics Letters A 15, № 31 (2000): 1923–30. http://dx.doi.org/10.1142/s0217732300002346.

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We propose a new approach based on the algebraization of the associated Lamé equation [Formula: see text] within sl(2, ℝ) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m, l. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer l.

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18

Pawellek, Michael. "Quasi-doubly periodic solutions to a generalized Lamé equation." Journal of Physics A: Mathematical and Theoretical 40, no. 27 (2007): 7673–86. http://dx.doi.org/10.1088/1751-8113/40/27/016.

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19

Chen, Zhijie, Ting-Jung Kuo, Chang-Shou Lin, and Kouichi Takemura. "On reducible monodromy representations of some generalized Lamé equation." Mathematische Zeitschrift 288, no. 3-4 (2017): 679–88. http://dx.doi.org/10.1007/s00209-017-1906-z.

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20

Ohmiya, M., H. Ohkura, D. Okaue, D. Saitoh, and T. Shiba. "Benjamin–Feir type instability of Sine–Gordon equation and spectrum of Lamé equation." Journal of Computational and Applied Mathematics 207, no. 2 (2007): 345–51. http://dx.doi.org/10.1016/j.cam.2006.10.009.

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21

Xiang, Chunhuan. "Travelling wave solutions of reduced super-KdV equation: A perspective from Lamé equation." Applied Mathematics and Computation 217, no. 1 (2010): 42–47. http://dx.doi.org/10.1016/j.amc.2010.05.041.

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22

Danielewski, Marek, and Bartłomiej Wierzba. "Mechano-Chemistry; Interdiffusion in Solid Solutions." Defect and Diffusion Forum 277 (April 2008): 61–68. http://dx.doi.org/10.4028/www.scientific.net/ddf.277.61.

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In this work we show that the volume velocity, ρυ , rather than the local centre of mass velocity should be used in continua. We use the volume continuity equation to define the volume frame of reference in the multicomponent, compressible continua. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every cont

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23

Chiang, Yik-Man, and Guo-Fu Yu. "Galoisian approach to complex oscillation theory of some Hill equations." MATHEMATICA SCANDINAVICA 124, no. 1 (2019): 102–31. http://dx.doi.org/10.7146/math.scand.a-110889.

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We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponent of convergence of zeros) of certain Hill equations considered by Bank and Laine using Nevanlinna theory must be Liouvillian solutions. These are solutions obtainable by suitable differential field extension constructions. In particular, we establish a full correspondence between solutions of non-oscillatory type and Liouvillian solutions for a particular Hill equation. Explicit closed-form solutions are obtained via both methods for this Hill equation whose potential

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24

Aksyuk, I. A., A. E. Kireeva, K. K. Sabelfeld, and D. D. Smirnov. "Stochastic Simulation Algorithms for Iterative Solution of the Lamé Equation." Numerical Analysis and Applications 16, no. 4 (2023): 299–316. http://dx.doi.org/10.1134/s199542392304002x.

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25

Zsuppán, Sándor. "Examples for an extended Barabási-Albert model with random initial degrees." Dimenziók: matematikai közlemények 8 (2020): 3–13. http://dx.doi.org/10.20312/dim.2020.01.

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We develop a Papkovich-Neuber type representation formula for the solutions of the Navier-Lamé equation of linear elastostatics for spatial star-shaped domains. This representation is compared to the existing ones.

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26

Cassano, Biagio, Lucrezia Cossetti, and Luca Fanelli. "Spectral enclosures for the damped elastic wave equation." Mathematics in Engineering 4, no. 6 (2022): 1–10. http://dx.doi.org/10.3934/mine.2022052.

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<abstract><p>In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lamé operators with non self-adjoint perturbations, we provide quantitative bounds on the location of the point spectrum in terms of suitable norms of the damping coefficient.</p></abstract>

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27

Свердлов, С. Ю. "АНАЛІЗ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ КОНСОЛЬНОЇ ПЛИТИ З ЛІНІЙНИМ ПІДШИПНИКОВИМ З’ЄДНАННЯМ". Open Information and Computer Integrated Technologies, № 104 (3 липня 2025): 82–96. https://doi.org/10.32620/oikit.2025.104.06.

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A methodology for solving a spatial problem of elasticity theory for a slab with a rigid embedded cylindrical fixation and a bearing connection is proposed. The computational model is represented as a layer with a longitudinal cylindrical cavity and a longitudinal cylindrical thick-walled pipe. Stresses are specified at the upper and lower boundaries of the layer, displacements are specified on the surface of the cavity, and contact-type conditions are specified on the inner surface of the pipe. The layer and the pipe are rigidly connected to each other. The solution to the problem is presente

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28

Benramdane, Amina, Nadia Mezouar, Mohammed Sulaiman Alqawba, Salah Mahmoud Boulaaras, and Bahri Belkacem Cherif. "Blow-Up for a Stochastic Viscoelastic Lamé Equation with Logarithmic Nonlinearity." Journal of Function Spaces 2021 (April 17, 2021): 1–10. http://dx.doi.org/10.1155/2021/9943969.

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In this paper, we consider an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and logarithmic nonlinear source terms. We proved a blow-up result for the solution with decreasing kernel.

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29

Penskoi, A. "Extremal Spectral Properties of Lawson Tau-Surfaces and the Lamé Equation." Moscow Mathematical Journal 12, no. 1 (2012): 173–92. http://dx.doi.org/10.17323/1609-4514-2012-12-1-173-192.

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30

Loray, F. "Isomonodromic deformation of Lamé connections, Painlevé VI equation and Okamoto symmetry." Izvestiya: Mathematics 80, no. 1 (2016): 113–66. http://dx.doi.org/10.1070/im8310.

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31

Kweon, Jae Ryong. "For the parabolic Lamé system on polygonal domains: The transport equation." Journal of Differential Equations 255, no. 6 (2013): 1109–31. http://dx.doi.org/10.1016/j.jde.2013.05.017.

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32

Ganguly, A., M. V. Ioffe, and L. M. Nieto. "A new effective mass Hamiltonian and associated Lamé equation: bound states." Journal of Physics A: Mathematical and General 39, no. 47 (2006): 14659–80. http://dx.doi.org/10.1088/0305-4470/39/47/010.

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33

Joshi, Nalini, and Andrew Pickering. "Generalized Halphen systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 6 (2006): 1287–301. http://dx.doi.org/10.1017/s0308210500004984.

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Towards the end of the nineteenth century, Halphen studied a remarkable sequence of higher-order linear equations with doubly periodic coefficients, generalizations of a certain Lamé equation, having the property that quotients of solutions are single valued. Here we consider further generalizations where, instead of the Weierstrass ℘-function, the coefficients depend on the first Painlevé transcendent. Using these equations, we obtain new higher-order systems of nonlinear equations having the Painlevé property. We also give new results on the interpretation of the Painlevé tests with regard t

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34

BRIHAYE, YVES, and BETTI HARTMANN. "QUASI-EXACTLY SOLVABLE N×N-MATRIX SCHRÖDINGER OPERATORS." Modern Physics Letters A 16, no. 29 (2001): 1895–906. http://dx.doi.org/10.1142/s0217732301005242.

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New examples of matrix quasi-exactly solvable Schrödinger operators are constructed. One of them constitutes a matrix generalization of the quasi-exactly solvable anharmonic oscillator, the corresponding invariant vector space is constructed explicitly. Matrix generalizations of the Lamé equation are also investigated.

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35

SREE RANJANI, S., A. K. KAPOOR, and P. K. PANIGRAHI. "BAND EDGE EIGENFUNCTIONS AND EIGENVALUES FOR PERIODIC POTENTIALS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM." Modern Physics Letters A 19, no. 27 (2004): 2047–58. http://dx.doi.org/10.1142/s0217732304014197.

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We demonstrate the procedure of finding the band edge eigenfunctions and eigenvalues of periodic potentials, through the quantum Hamilton–Jacobi formalism. The potentials studied here are the Lamé and associated Lamé, which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function p, obeying a Riccati type equation in the complex x-plane. Essential use is made of suitable conformal transformations, which lead to the eigenvalues and the eigenfunctions corresponding to the band edges, in a straightforward man

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36

Bagapsh, A. O. "On the Geometric Properties of the Poisson Kernel for the Lamé Equation." Computational Mathematics and Mathematical Physics 59, no. 12 (2019): 2124–44. http://dx.doi.org/10.1134/s0965542519120042.

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37

Chen, J. T., Y. T. Lee, and K. H. Chou. "Revisit of Two Classical Elasticity Problems by using the Null-Field Boundary Integral Equations." Journal of Mechanics 26, no. 3 (2010): 393–401. http://dx.doi.org/10.1017/s1727719100003956.

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AbstractIn this paper, the two classical elasticity problems, Lamé problem and stress concentration factor, are revisited by using the null-field boundary integral equation (BIE). The null-field boundary integral formulation is utilized in conjunction with degenerate kernels and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. In the two classical problems of elasticity, the null-field BIE is employed to derive the exact solutions. The Kelvin solution is first

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38

Hortaçsu, M. "Heun Functions and Some of Their Applications in Physics." Advances in High Energy Physics 2018 (July 19, 2018): 1–14. http://dx.doi.org/10.1155/2018/8621573.

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Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations. There are important examples, however, where one has to use higher order equations. Heun equation is

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39

Ilmenkov, Sergey L., Sergey A. Pereselkov, Vladimir I. Grachev, and Nikolay V. Ladykin. "Sound reflection from an elastic finite cylindrical shell of different relative lengths." Radioelectronics. Nanosystems. Information Technologies. 15, no. 4 (2023): 425–32. http://dx.doi.org/10.17725/rensit.2023.15.425.

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A calculation of the sound pressure frequency dependences scattered by a finite elastic cylindrical shell placed in a liquid medium is presented. The shell has hemispherical ends and is considered either hollow or filled with gas or liquid. The scattered sound pressure under conditions of hydroelastic contact on the shell surfaces is found by jointly using the Kirchhoff integral and the integral equation for the elastic medium displacement vector, obeying the Lamé equation. Boundary conditions regarding stresses and displacements are formulated for each of the shell contact surfaces with the e

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40

de Hoop, Maarten V., and Alexei Iantchenko. "Inverse problem for the Rayleigh system with spectral data." Journal of Mathematical Physics 63, no. 3 (2022): 031505. http://dx.doi.org/10.1063/5.0055827.

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We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lamé parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution, while the data are captured in a Jost function, and we point out parallels with a corresponding problem for the Schrödinger equation. The Jost function can be identified with spectral data. We derive a Gel’fand-Levitan type equation and obtain uniqueness with two distinct frequencies.

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41

BRIHAYE, YVES. "QUASI-EXACTLY SOLVABLE MATRIX SCHRÖDINGER OPERATORS." Modern Physics Letters A 15, no. 26 (2000): 1647–53. http://dx.doi.org/10.1142/s0217732300002073.

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Two families of quasi-exactly solvable 2×2 matrix Schrödinger operators are constructed. The first one is based on a polynomial matrix potential and depends on three parameters. The second is a one-parameter generalization of the scalar Lamé equation. The relationship between these operators and QES Hamiltonians already considered in the literature is pointed out.

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42

Мірошніков, В. Ю., О. Б. Савін, М. Л. Косенко та О. О. Ільїн. "АНАЛІЗ НАПРУЖЕНОГО СТАНУ ШАРУ З ДВОМА ЦИЛІНДРИЧНИМИ ВРІЗАНИМИ ОПОРАМИ ТА ЦИЛІНДРИЧНИМИ ВТУЛКАМИ". Open Information and Computer Integrated Technologies, № 101 (9 грудня 2024): 112–26. https://doi.org/10.32620/oikit.2024.101.08.

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The spatial problem of the theory of elasticity for a layer on cylindrical embedded supports with cylindrical sleeves (thick-walled pipes) located between each support and the layer is solved. Smooth contact conditions are set at the interface between the layer and the pipes. Stresses are specified on the surfaces of the layer, and displacements are specified on the inner surface of the pipe (rigidly conjugated to the support). The analytical and numerical solution of the problem is based on the Lamé equations written for the layer and each pipe. When the boundary conditions and the conditions

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43

Romanov, V. G., and M. Yamamoto. "Recovering a Lamé kernel in a viscoelastic equation by a single boundary measurement." Applicable Analysis 89, no. 3 (2010): 377–90. http://dx.doi.org/10.1080/00036810903518975.

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44

Costin, Rodica D. "Integrability properties of a generalized Lamé equation: Applications to the Henon–Heiles system." Methods and Applications of Analysis 4, no. 2 (1997): 113–23. http://dx.doi.org/10.4310/maa.1997.v4.n2.a1.

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45

Musso, Emilio, and Álvaro Pámpano. "Integrable flows on null curves in the Anti-de Sitter 3-space." Nonlinearity 37, no. 11 (2024): 115015. http://dx.doi.org/10.1088/1361-6544/ad7d58.

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Abstract We formulate integrable flows related to the Korteweg–De Vries (KdV) hierarchy on null curves in the anti-de Sitter 3-space ( AdS ). Exploiting the specific properties of the geometry of AdS , we analyze their interrelationships with Pinkall flows in centro-affine geometry. We show that closed stationary solutions of the lower order flow can be explicitly found in terms of periodic solutions of a Lamé equation. In addition, we study the evolution of non-stationary curves arising from a 3-parameter family of periodic solutions of the KdV equation.

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46

Taouaf, Noureddine, Noureddine Amroun, Abbes Benaissa, and Abderrahmane Beniani. "Well-posedness and exponential stability for coupled Lamé system with a viscoelastic damping." Filomat 32, no. 10 (2018): 3591–98. http://dx.doi.org/10.2298/fil1810591t.

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In this paper, we consider a coupled Lam? system with a viscoelastic damping in the first equation. We prove well-posedness by using Faedo-Galerkin method and establish an exponential decay result by introducing a suitable Lyaponov functional.

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47

Dassios, G., and A. S. Fokas. "The basic elliptic equations in an equilateral triangle." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2061 (2005): 2721–48. http://dx.doi.org/10.1098/rspa.2005.1466.

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In his deep and prolific investigations of heat diffusion, Lamé was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular, he derived explicit results for the Dirichlet and Neumann cases using an ingenious change of variables. The relevant eigenfunctions are a complicated infinite series in terms of his variables. Here we first show that boundary-value problems with simple boundary conditions, such as the Dirichlet and the Neumann problems, can be solved in an elementary manner. In particular, the unknown Neumann and Di

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48

Zieniuk, Eugeniusz, and Agnieszka Bołtuc. "Modification of the boundary integral equation for the Navier-Lamé equations in 2D elastoplastic problems and its numerical solving." International Journal for Numerical Methods in Engineering 110, no. 12 (2017): 1173–200. http://dx.doi.org/10.1002/nme.5451.

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49

Chen, Zhijie, Ting-Jung Kuo, and Chang-Shou Lin. "The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application." Journal de Mathématiques Pures et Appliquées 132 (December 2019): 251–72. http://dx.doi.org/10.1016/j.matpur.2019.05.004.

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50

Wang, Lin, David A. Ratkowsky, Johan Gielis, Paolo Emilio Ricci, and Peijian Shi. "Effects of the Numerical Values of the Parameters in the Gielis Equation on Its Geometries." Symmetry 14, no. 12 (2022): 2475. http://dx.doi.org/10.3390/sym14122475.

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The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equa

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