Singular Perturbations of Boundary Value Problems Involving Ordinary Differential Equations [PDF]
Journal of the Society for Industrial and Applied Mathematics, 1963 In this lecture we shall consider boundary value problems Pe in which the order of the differential equation drops, or its type changes, as e → 0 so that the boundary conditions prescribed in Pe are not appropriate when e = 0, and it is not at all obvious how P0 should be defined.
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Slowly varying oscillators [PDF]
, 1985 We develop a Melnikov type perturbation method for detecting periodic and homoclinic orbits and codimension one bifurcations in a class of third order nonlinear ordinary differential equations.
Holmes, Philip, Wiggins, Stephen
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Studies of Solutions of Singularly Perturbed Ordinary Differential Equations
Bulletin of Science and Practice, 2023 The eigenvalues of the Jordan matrix determine different types of stability. It is not always possible to obtain asymptotic estimates in the real axis. Therefore, in this paper we will consider the types of stability that can be estimated in the real axis.
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Geometric optics and instability for semi-classical Schrodinger equations
, 2005 We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the ...
A. Majda +25 more
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Transporting non-Gaussianity from sub to super-horizon scales
, 2013 We extend the `moment transport method' for calculating the statistics of inflationary perturbations to the quantum phase of evolution on sub-horizon scales.
Mulryne, David J.
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Perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model [PDF]
, 2013 We study the perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model.
Marcos A Ramirez +2 more
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A ghost perturbation scheme to solve ordinary differential equations [PDF]
, 2022 Pedro L. Garrido
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Variational Approach to the Modulational Instability
, 2004 We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude and phase of ...
A. Hasegawa +35 more
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Stability Analysis of New Solutions of the EYM system with Cosmological Constant [PDF]
, 1996 We analyze the stability properties of the purely magnetic, static solutions to the Einstein--Yang--Mills equations with cosmological constant. It is shown that all three classes of solutions found in a recent study are unstable under spherical ...
G. Lavrelashvili +4 more
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Time after time – circadian clocks through the lens of oscillator theory
FEBS Letters, EarlyView.Oscillator theory bridges physics and circadian biology. Damped oscillators require external drivers, while limit cycles emerge from delayed feedback and nonlinearities. Coupling enables tissue‐level coherence, and entrainment aligns internal clocks with environmental cues.
Marta del Olmo +2 more
wiley +1 more source