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We prove local in time Strichartz estimates for the Dirac equation on spherically symmetric manifolds. As an application, we give a result of local well-posedness for some nonlinear models.

Analysis of PDEs · Mathematics 2019-02-21 Federico Cacciafesta , Anne-Sophie de Suzzoni

We formulate and discuss integrable analogue of the sine-Gordon equation on arbitrary time scales. This unification contains the sine-Gordon equation, discrete sine-Gordon equation and the Hirota equation (doubly discrete sine-Gordon…

Exactly Solvable and Integrable Systems · Physics 2014-04-15 Jan L. Cieśliński , Tomasz Nikiciuk , Kamil Waśkiewicz

Let $M=(0,\infty)_r\times Y$ be a $d$-dimensional ($d\ge 3$) metric cone with metric<br/>$g=dr^2+r^2h$, where $(Y,h)$ is a closed Riemannian manifold. Let<br/>$H=\Delta+V_0/r^2$ be the associated Schrodinger operator, with<br/>$V_0\in…

Analysis of PDEs · Mathematics 2025-11-25 Dangyang He

We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on negatively curved compact manifolds which improve the classical universal results results of Burq, G\'erard and Tzvetkov [11] in this geometry. In the…

Analysis of PDEs · Mathematics 2023-04-12 Matthew D. Blair , Xiaoqi Huang , Christopher D. Sogge

We present the exact solution of the Klein-Gordon equation in D-dimensions in the presence of the noncentral equal scalar and vector pseudoharmonic potential plus the new ring-shaped potential using the Nikiforov-Uvarov method. We obtain…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair , Ramazan Sever

We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein-Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to…

Analysis of PDEs · Mathematics 2020-09-22 Hans Lindblad , Jonas Luhrmann , Avy Soffer

The Klein-Gordon equation is solved approximately for the Hulth\'{e}n potential for any angular momentum quantum number $\ell$ with the position-dependent mass. Solutions are obtained reducing the Klein-Gordon equation into a…

Mathematical Physics · Physics 2009-11-13 Altug Arda , Ramazan Sever , Cevdet Tezcan

We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the…

General Relativity and Quantum Cosmology · Physics 2016-02-10 Ivan Kolar , Pavel Krtous

The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can…

Mathematical Physics · Physics 2008-11-26 J. Dittrich , P. Duclos

The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure…

Mathematical Physics · Physics 2015-05-13 M. R. Setare , O. Hatami

In this note, we consider discrete nonlinear Klein-Gordon equations with potential. By the pioneering work of Sigal, it is known that for the "continuous" nonlinear Klein-Gordon equation, no small time periodic solution exists generically.…

Analysis of PDEs · Mathematics 2016-03-08 Masaya Maeda

We have investigated the reality of exact bound states of complex and/or PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The Klein-Gordon equation has been solved by using the Nikiforov-Uvarov method which is…

Quantum Physics · Physics 2007-05-23 Mehmet Simsek , Harun Egrifes

We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…

General Relativity and Quantum Cosmology · Physics 2021-11-01 Benito A. Juárez-Aubry

We derive a uniform exponential decay of the total energy for the nonlinear Klein-Gordon equation with a damping around spatial infinity in the whole space or in the exterior of a star shaped obstacle.

Analysis of PDEs · Mathematics 2010-01-05 Lassaad Aloui , Slim Ibrahim , Kenji Nakanishi

We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…

High Energy Physics - Theory · Physics 2024-03-15 Shi-Dong Liang

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth…

Analysis of PDEs · Mathematics 2009-06-22 Axel Gruenrock , Hartmut Pecher

We derive the Klein--Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein--Gordon equation first using the Einstein…

Astrophysics · Physics 2009-06-23 Karim A. Malik , David Seery , Kishore N. Ananda

We derive an explicit manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of…

Quantum Physics · Physics 2008-11-26 A. Mostafazadeh , F. Zamani

The one-dimensional effective-mass Klein-Gordon equation for the real, and non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the…

Quantum Physics · Physics 2015-05-20 Altug Arda , Ramazan Sever

In a recent paper by Barton (J. Phys. A40, 1011 (2007)), the 1-dimensional Klein-Gordon equation was solved analytically for the non-singular Coulomb-like potential V_1(|x|) = -\alpha/(|x|+a). In the present paper, these results are…

Mathematical Physics · Physics 2009-11-13 Richard L. Hall