Results 11 to 20 of about 185 (48)

A Spectral Gap Estimate and Applications

, 2017
We consider the Schr\"odinger operator $$-\frac{d^2}{d x^2} + V \qquad \mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions},$$ where $V$ is bounded from below and prove a lower bound on the first eigenvalue $\lambda_1$ in terms of ...
Georgiev, Bogdan, Mukherjee, Mayukh, Steinerberger, Stefan   +2 more
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Uniqueness and stability results for an inverse spectral problem in a periodic waveguide [PDF]

, 2015
Let $\Omega =\omega\times\mathbb R$ where $\omega\subset \mathbb R^2$ be a bounded domain, and $V : \Omega \to\mathbb R$ a bounded potential which is $2\pi$-periodic in the variable $x_{3}\in \mathbb R$.
Kavian, Otared, Kian, Yavar, Soccorsi, Eric   +2 more
core   +3 more sources

Mathematical analysis of some new adequate broad-ranging soliton solutions of nonlinear models through the recent technique

Partial Differential Equations in Applied Mathematics
The Bogoyavlenskii and the simplified modified Camassa-Holm (SMCH) models are studied through the recent technique namely auxiliary equation method in this paper.
M. Ashikur Rahman, M. Al-Amin, Mst. Kamrunnaher, M. Abul Kawser, Rajaul Haque, M. Ali Akbar, M. Nurul Islam   +6 more
doaj   +1 more source

Computational analysis and wave propagation behavior of hyper-geometric soliton waves in plasma physics via the auxiliary equation method

Partial Differential Equations in Applied Mathematics
This study investigate the widely used nonlinear fractional Kairat-II (K-II) model, which is used to explain the differential geometry of curves and equivalence aspects.
M. Al-Amin, M. Nurul Islam, M. Ali Akbar
doaj   +1 more source

The asymptotic limits of zero modes of massless Dirac operators

, 2007
Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $ D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \
A.A. Balinsky, A.A. Balinsky, C. Adam, C. Adam, C. Adam, D.M. Elton, J. Fröhlich, L. Bugliaro, L. Erdös, L. Erdös, L. Erdös, M. Loss, Tomio Umeda, Yoshimi Saitō   +13 more
core   +2 more sources

Carleson Measures and Logvinenko-Sereda sets on compact manifolds [PDF]

, 2010
Given a compact Riemannian manifold $M$ of dimension $m\geq 2$, we study the space of functions of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L\geq 1$ associated to the Laplace-Beltrami operator on $M$.
Ortega-Cerdà, Joaquim, Pridhnani, Bharti   +1 more
core   +2 more sources

Multiple Aharonov--Bohm eigenvalues: the case of the first eigenvalue on the disk

, 2018
It is known that the first eigenvalue for Aharonov--Bohm operators with half-integer circulation in the unit disk is double if the potential's pole is located at the origin. We prove that in fact it is simple as the pole $a\neq 0$
Abatangelo, Laura
core   +1 more source

Laplacian eigenvalues functionals and metric deformations on compact manifolds [PDF]

, 2007
In this paper, we investigate critical points of the Laplacian's eigenvalues considered as functionals on the space of Riemmannian metrics or a conformal class of metrics on a compact manifold.
Agricola, Ahmad El Soufi, Bando, Berger, Bérard-Bergery, Colbois, Colbois, Colin de Verdière, Eells, Eells, El Soufi, El Soufi, El Soufi, El Soufi, El Soufi, Ferus, Friedlander, Girouard, Grigoryan, Hersch, Hsiang, Jakobson, Korevaar, Li, Mutô, Mutō, Nadirashvili, Park, Saïd Ilias, Takahashi, Tanno, Toth, Urakawa, Yang   +33 more
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On occurrence of spectral edges for periodic operators inside the Brillouin zone [PDF]

, 2007
The article discusses the following frequently arising question on the spectral structure of periodic operators of mathematical physics (e.g., Schroedinger, Maxwell, waveguide operators, etc.). Is it true that one can obtain the correct spectrum by using
, A Sobolev, Ashcroft N W, B Winn, Busch K von Freyman G Linden S Mingaleev S F Tkeshelashvili L Wegener M, Chung F, Colin de Verdière Y, Colin de Verdière Y, Dell'Antonio G Tenuta L, Eastham M S P, Exner P Šeba P, Freidlin M, Freidlin M, Grieser Daniel, Helffer B, Helffer B, Helffer B, Hempel R, J M Harrison, Jackson J D, Joannopoulos J D, Johnson S G, Kato T, Klopp F, Kuchment P, Kuchment P, Kuchment P, Kuchment P, Kuchment P, Kuchment P, Kuchment P, Kuchment P, Molchanov S, Molchanov S Vainberg B, Molchanov S Vainberg B, Novikov S P, P Kuchment, Reed M, Rubinstein J, Rubinstein J, Rubinstein J, Saito Y, Saito Y, Skriganov M, Zeng H   +44 more
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Hearing the shape of a triangle

, 2013
In 1966 Mark Kac asked the famous question 'Can one hear the shape of a drum?'. While this was later shown to be false in general, it was proved by C. Durso that one can hear the shape of a triangle.
Grieser, Daniel, Maronna, Svenja
core   +1 more source