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Showing 1 to 20 of 40 for “"Klein-Gordon"”.
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Ratchet dynamics in nonlinear Klein-Gordon systems
… was focused on the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic and asymmetric lattice of point-like inhomogeneities in the overdamped regime. In addition, we explained the underlying rectification mechanism within a collective coordinate framework, which shows that such a system …
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Stability of periodic solutions to nonlinear Klein-Gordon equations
… periodic travelling wave solutions to nonlinear Klein-Gordon equations, subject to small and localized perturbations. Using the periodic Evans function technique, we analyze the spectrum of a linearized quadratic eigenvalue pencil associated with the linearized equation, in a neighbourhood of the …
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A Numerical Method for Computing Radially Symmetric Solutions of a Dissipative Nonlinear Modified Klein-Gordon Equation
… solutions of a dissipative nonlinear modified Klein-Gordon equation in an open sphere around the origin, with constant internal and external damping coefficients and nonlinear term of the form G' (w) = w ^p, with p an odd number greater than 1. We prove that our scheme is consistent of …
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ERROR ESTIMATES OF NUMERICAL METHODS FOR THE LONG-TIME DYNAMICS OF THE NONLINEAR KLEIN-GORDON EQUATION
… for the long-time dynamics of the nonlinear Klein-Gordon equation (NKGE) with weak nonlinearity, which is characterized by $\varepsilon^2$ with $\varepsilon \in (0, 1]$ a dimensionless parameter.The analytical results indicate that the life-span of a smooth solution to this NKGE is at least …
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I. A pressure Poisson method for the incompressible Navier-Stokes equations : II. Long time behavior of the Klein-Gordon equations
… we examine the long time behavior of the Klein-Gordon equation with various nonlinearities. In the first case, we show that for a positive (repulsive) strong nonlinearity, the system thermalizes into a state which exhibits characteristics of linear waves. Through the introduction of a …
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Mode stabilities and instabilities for scalar fields on Kerr exterior spacetimes
In this thesis we study wave and Klein-Gordon equations on Kerr exterior spacetimes. For the wave equation, we give a quantitative refinement and simple proofs of mode stability type statements on Kerr backgrounds in the full sub-extremal range ([absolute value of]a < M). As an application, we are …
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Coupled mode reductions and rotating wave approximations in nonlinear equations
… Next, we consider a class of discrete nonlinear Klein-Gordon equations with damping and parametric drive. Using small amplitude ansatzs, one usually approximates the equations using a damped, driven discrete nonlinear Schrodinger type equation. Here, we show for the first time the justification …
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Transição súbita e quebra de aproximação modulacional em sitemas espaço-temporais
… súbita para o caos na equação não linear de Klein Gordon são estudados. É analisada a influência da presença de caos sobre a incoerência no problema da interação de um tripleto de ondas quando um modelo de aproximação adiabática deixa de ser válido. É encontrado um limiar para o valor do …
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Decay for quasilinear wave equations on cosmological black hole backgrounds
… constant. Specifically, we study the Klein Gordon equation with mass $\mu^2_{\textit{KG}}\geq 0$ and the quasilinear wave equation which respectively read \begin{equation*} \Box_{g}\psi-\mu^2_{\textit{KG}}\psi=0,\qquad \Box_{g(\nabla\psi)}\psi=\partial\psi\cdot\partial\psi. …
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Global Positioning System in Curved Space-Time and Other Applications of General Relativity
… evolution of a three-dimensional Einstein-Klein-Gordon field.
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TWO RESULTS ON THE GLOBAL DYNAMICS OF PDES ON THE CIRCLE.
… limit of the one-dimensional cubic nonlinear Klein-Gordon equation, which is known (formally) to converge to the cubic nonlinear Schrödinger equation as c → ∞. More precisely, it is known that smooth solutions of the Klein-Gordon equation converge over compact intervals of time to solutions …
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The free particle on q-Minkowski space
… erfolgreiches Konzept in der Physik. Bei sehr kleinen Abständen jedoch ist auch diese Struktur einer Quantisierung unterworfen, und man muß nach neuen physikalischen Modellen zu ihrer Beschreibung suchen. Eine Möglichkeit ist es, den Raum durch eine nichtkommutative Algebra darzustellen und auf …
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Scattering at threshold in massive wave propagation and ionization
… with an attractive long range potential and the Klein–Gordon equation. In the former case, the transition occurs as the spectral parameter 𝐸 → 0⁺, and thus describes the ionization of Hydrogenic atoms, and in the latter case the transition occurs at null infinity, where the phase in the …
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Numerical Reconstruction and Applications of Acoustic and Electromagnetic Ultra-Wideband Localized Pulses Generated by Dynamic Aperture Antennas
… through dispersive media modeled by the Klein-Gordon equation. It is demonstrated that contrary to expectation, the depletion of the spectral components of the LW Klein-Gordon field may be slower than that associated with the free space scalar field. Previous work by Power et al. [73] is …
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Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field
… solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or …
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ERROR BOUNDS OF COMPACT FINITE DIFFERENCE METHODS FOR SOME DISPERSIVE PDEs AND APPLICATIONS
… dispersive PDEs, including the nonlinear Klein-Gordon equation in the nonrelativistic regime and the Zakharov system in the subsonic regime. Proofs of error estimate based on energy methods and cut-off techniques are presented, and numerical results are reported for verification purposes. …
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Instabilities in asymptotically AdS spacetimes
… $(\mathcal{M},g_{\mathrm{KAdS}})$, in which the Klein-Gordon equation \begin{align*} \Box_g\psi+\frac{\alpha}{\ell^2}\psi=0 \end{align*} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound …
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Asymptotic analysis of the parametrically driven damped nonlinear evolution equation
… nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear oscillator, we apply the Lindstedt-Poincare method and the multiple-scales technique to obtain the amplitude equation …
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Numerical Methods and Their Analysis for Some Nonlinear Dispersive Equations
… Schrodinger-Poisson (SP) type system, the Klein-Gordon (KG) equation, the sine-Gordon (SG) and perturbed Schrodinger (PNLS) equations. For SP type system, various numerical methods were compared for ground states calculation and dynamics, in both nonrelativistic and relativistic cases. …
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ELASTIC SCATTERING AT RELATIVISTIC ENERGIES OF ALPHA PARTICLES AND PIONS BY NUCLEI USING AN OPTICAL POTENTIAL
… elastic scattering cross sections using the Klein-Gordon equation. The reason for writing this code is because existing codes do not include relativistic kinematics and therefore are only valid for lower energies. This code was used to analyze alpha particle and pion scattering at …
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